For a wpse question: only allow password protected posts to be published.

password-only.php

<?php
/*
Plugin Name: Passworded Posts Only (for wpse38806)
Author: Christopher Davis
Author URI: http://www.christopherguitar.net/
License: GPL2
*/

add_action( 'admin_print_scripts-post.php', 'wpse38806_enqueue_js' );
add_action( 'admin_print_scripts-post-new.php', 'wpse38806_enqueue_js' );
function wpse38806_enqueue_js()
{
    if( 'post' != get_post_type() ) return;
    
    wp_enqueue_script(
        'wpse38806js',
        plugin_dir_url( __FILE__ ) . 'private.js',
        array( 'jquery' ),
        NULL,
        true
    );
}


add_action('add_meta_boxes_post', 'wpse38806_hijack_meta_boxes' );
function wpse38806_hijack_meta_boxes( $post )
{
    remove_meta_box( 'submitdiv', $post->post_type, 'side' );
    add_meta_box('submitdiv-2', __('Publish'), 'wpse38806_post_submit_meta_box', $post->post_type, 'side', 'high');
}

function wpse38806_post_submit_meta_box($post) {
	global $action;

	$post_type = $post->post_type;
	$post_type_object = get_post_type_object($post_type);
	$can_publish = current_user_can($post_type_object->cap->publish_posts);
?>
<div class="submitbox" id="submitpost">

<div id="minor-publishing">

<?php // Hidden submit button early on so that the browser chooses the right button when form is submitted with Return key ?>
<div style="display:none;">
<?php submit_button( __( 'Save' ), 'button', 'save' ); ?>
</div>

<div id="minor-publishing-actions">
<div id="save-action">
<?php if ( 'publish' != $post->post_status && 'future' != $post->post_status && 'pending' != $post->post_status )  { ?>
<input <?php if ( 'private' == $post->post_status ) { ?>style="display:none"<?php } ?> type="submit" name="save" id="save-post" value="<?php esc_attr_e('Save Draft'); ?>" tabindex="4" class="button button-highlighted" />
<?php } elseif ( 'pending' == $post->post_status && $can_publish ) { ?>
<input type="submit" name="save" id="save-post" value="<?php esc_attr_e('Save as Pending'); ?>" tabindex="4" class="button button-highlighted" />
<?php } ?>
<img src="<?php echo esc_url( admin_url( 'images/wpspin_light.gif' ) ); ?>" class="ajax-loading" id="draft-ajax-loading" alt="" />
</div>

<div id="preview-action">
<?php
if ( 'publish' == $post->post_status ) {
	$preview_link = esc_url( get_permalink( $post->ID ) );
	$preview_button = __( 'Preview Changes' );
} else {
	$preview_link = get_permalink( $post->ID );
	if ( is_ssl() )
		$preview_link = str_replace( 'http://', 'https://', $preview_link );
	$preview_link = esc_url( apply_filters( 'preview_post_link', add_query_arg( 'preview', 'true', $preview_link ) ) );
	$preview_button = __( 'Preview' );
}
?>
<a class="preview button" href="<?php echo $preview_link; ?>" target="wp-preview" id="post-preview" tabindex="4"><?php echo $preview_button; ?></a>
<input type="hidden" name="wp-preview" id="wp-preview" value="" />
</div>

<div class="clear"></div>
</div><?php // /minor-publishing-actions ?>

<div id="misc-publishing-actions">

<div class="misc-pub-section<?php if ( !$can_publish ) { echo ' misc-pub-section-last'; } ?>"><label for="post_status"><?php _e('Status:') ?></label>
<span id="post-status-display">
<?php
switch ( $post->post_status ) {
	case 'private':
		_e('Privately Published');
		break;
	case 'publish':
		_e('Published');
		break;
	case 'future':
		_e('Scheduled');
		break;
	case 'pending':
		_e('Pending Review');
		break;
	case 'draft':
	case 'auto-draft':
		_e('Draft');
		break;
}
?>
</span>
<?php if ( 'publish' == $post->post_status || 'private' == $post->post_status || $can_publish ) { ?>
<a href="#post_status" <?php if ( 'private' == $post->post_status ) { ?>style="display:none;" <?php } ?>class="edit-post-status hide-if-no-js" tabindex='4'><?php _e('Edit') ?></a>

<div id="post-status-select" class="hide-if-js">
<input type="hidden" name="hidden_post_status" id="hidden_post_status" value="<?php echo esc_attr( ('auto-draft' == $post->post_status ) ? 'draft' : $post->post_status); ?>" />
<select name='post_status' id='post_status' tabindex='4'>
<?php if ( 'publish' == $post->post_status ) : ?>
<option<?php selected( $post->post_status, 'publish' ); ?> value='publish'><?php _e('Published') ?></option>
<?php elseif ( 'private' == $post->post_status ) : ?>
<option<?php selected( $post->post_status, 'private' ); ?> value='publish'><?php _e('Privately Published') ?></option>
<?php elseif ( 'future' == $post->post_status ) : ?>
<option<?php selected( $post->post_status, 'future' ); ?> value='future'><?php _e('Scheduled') ?></option>
<?php endif; ?>
<option<?php selected( $post->post_status, 'pending' ); ?> value='pending'><?php _e('Pending Review') ?></option>
<?php if ( 'auto-draft' == $post->post_status ) : ?>
<option<?php selected( $post->post_status, 'auto-draft' ); ?> value='draft'><?php _e('Draft') ?></option>
<?php else : ?>
<option<?php selected( $post->post_status, 'draft' ); ?> value='draft'><?php _e('Draft') ?></option>
<?php endif; ?>
</select>
 <a href="#post_status" class="save-post-status hide-if-no-js button"><?php _e('OK'); ?></a>
 <a href="#post_status" class="cancel-post-status hide-if-no-js"><?php _e('Cancel'); ?></a>
</div>

<?php } ?>
</div><?php // /misc-pub-section ?>

<div class="misc-pub-section " id="visibility">
<?php if ( $can_publish ) { ?>

<div id="post-visibility-select" class="hide-if-js" style="display:block">
<input type="hidden" name="hidden_post_password" id="hidden-post-password" value="<?php echo esc_attr($post->post_password); ?>" />
<?php if ($post_type == 'post'): ?>
<input type="checkbox" style="display:none" name="hidden_post_sticky" id="hidden-post-sticky" value="sticky" <?php checked(is_sticky($post->ID)); ?> />
<?php endif; ?>
<input type="hidden" name="hidden_post_visibility" id="hidden-post-visibility" value="<?php echo esc_attr( $visibility ); ?>" />

<input type="radio" name="visibility" id="visibility-radio-password" value="password" <?php checked( $visibility, 'password' ); ?> /> <label for="visibility-radio-password" class="selectit"><?php _e('Password protected'); ?></label><br />
<span id="password-span" style="display:block"><label for="post_password"><?php _e('Password:'); ?></label> <input type="text" name="post_password" id="post_password" value="<?php echo esc_attr($post->post_password); ?>" /><br /></span>
</div>
<?php } ?>

</div><?php // /misc-pub-section ?>

<?php
// translators: Publish box date format, see http://php.net/date
$datef = __( 'M j, Y @ G:i' );
if ( 0 != $post->ID ) {
	if ( 'future' == $post->post_status ) { // scheduled for publishing at a future date
		$stamp = __('Scheduled for: <b>%1$s</b>');
	} else if ( 'publish' == $post->post_status || 'private' == $post->post_status ) { // already published
		$stamp = __('Published on: <b>%1$s</b>');
	} else if ( '0000-00-00 00:00:00' == $post->post_date_gmt ) { // draft, 1 or more saves, no date specified
		$stamp = __('Publish <b>immediately</b>');
	} else if ( time() < strtotime( $post->post_date_gmt . ' +0000' ) ) { // draft, 1 or more saves, future date specified
		$stamp = __('Schedule for: <b>%1$s</b>');
	} else { // draft, 1 or more saves, date specified
		$stamp = __('Publish on: <b>%1$s</b>');
	}
	$date = date_i18n( $datef, strtotime( $post->post_date ) );
} else { // draft (no saves, and thus no date specified)
	$stamp = __('Publish <b>immediately</b>');
	$date = date_i18n( $datef, strtotime( current_time('mysql') ) );
}

if ( $can_publish ) : // Contributors don't get to choose the date of publish ?>
<div class="misc-pub-section curtime misc-pub-section-last">
	<span id="timestamp">
	<?php printf($stamp, $date); ?></span>
	<a href="#edit_timestamp" class="edit-timestamp hide-if-no-js" tabindex='4'><?php _e('Edit') ?></a>
	<div id="timestampdiv" class="hide-if-js"><?php touch_time(($action == 'edit'),1,4); ?></div>
</div><?php // /misc-pub-section ?>
<?php endif; ?>

<?php do_action('post_submitbox_misc_actions'); ?>
</div>
<div class="clear"></div>
</div>

<div id="major-publishing-actions">
<?php do_action('post_submitbox_start'); ?>
<div id="delete-action">
<?php
if ( current_user_can( "delete_post", $post->ID ) ) {
	if ( !EMPTY_TRASH_DAYS )
		$delete_text = __('Delete Permanently');
	else
		$delete_text = __('Move to Trash');
	?>
<a class="submitdelete deletion" href="<?php echo get_delete_post_link($post->ID); ?>"><?php echo $delete_text; ?></a><?php
} ?>
</div>

<div id="publishing-action">
<img src="<?php echo esc_url( admin_url( 'images/wpspin_light.gif' ) ); ?>" class="ajax-loading" id="ajax-loading" alt="" />
<?php
if ( !in_array( $post->post_status, array('publish', 'future', 'private') ) || 0 == $post->ID ) {
	if ( $can_publish ) :
		if ( !empty($post->post_date_gmt) && time() < strtotime( $post->post_date_gmt . ' +0000' ) ) : ?>
		<input name="original_publish" type="hidden" id="original_publish" value="<?php esc_attr_e('Schedule') ?>" />
		<?php submit_button( __( 'Schedule' ), 'primary', 'publish', false, array( 'tabindex' => '5', 'accesskey' => 'p' ) ); ?>
<?php	else : ?>
		<input name="original_publish" type="hidden" id="original_publish" value="<?php esc_attr_e('Publish') ?>" />
		<?php submit_button( __( 'Publish' ), 'primary', 'publish', false, array( 'tabindex' => '5', 'accesskey' => 'p' ) ); ?>
<?php	endif;
	else : ?>
		<input name="original_publish" type="hidden" id="original_publish" value="<?php esc_attr_e('Submit for Review') ?>" />
		<?php submit_button( __( 'Submit for Review' ), 'primary', 'publish', false, array( 'tabindex' => '5', 'accesskey' => 'p' ) ); ?>
<?php
	endif;
} else { ?>
		<input name="original_publish" type="hidden" id="original_publish" value="<?php esc_attr_e('Update') ?>" />
		<input name="save" type="submit" class="button-primary" id="publish" tabindex="5" accesskey="p" value="<?php esc_attr_e('Update') ?>" />
<?php
} ?>
</div>
<div class="clear"></div>
</div>
</div>

<?php
}

private.js

jQuery(document).ready(function(){
    // hide the stuff you don't want
    jQuery('label[for=visibility-radio-public], label[for=visibility-radio-private]').hide();
    jQuery('input#visibility-radio-public, input#visibility-radio-private').hide();
    
    // trigger clicks to open the various things
    jQuery('a.edit-visibility').trigger('click');
    jQuery('input#visibility-radio-password').trigger('click');
    
    // stop form submission if there's no password, add an error message
    jQuery('form#post').submit(function(){
        if( ! jQuery('input#post_password').val() ){
            jQuery('img#ajax-loading').hide();
            jQuery('input#publish').removeClass('button-primary-disabled');
            jQuery('div.wrap h2').after('<div id="message" class="error"><p>Please enter a password!</p></div>');
            return false;
        }
    });
});