Widget code not working

I just wrote a new widget, but it is not working. I have written a bunch of widgets, but this one does not work and I cannot figure out why. The widget is part of a custom theme I am working on. The theme itself works fine, as do the other widgets I wrote with this theme. I wanted to add an additional widget to the theme. What happens is this:

The new theme installs and activates properly — no errors.

The new widget shows up on the widgets page, so far so good.

I drag the widget to a side bar, that works just fine.

I set the widgets parameters and then click save. That *seems* to work.

I visit the site. The site displays fine, but the widget does not.

(head scratching, hair pulling…)

Using Firebug I discover something odd. The POST for this new widget has widget_number set to -1. *NONE OF THE OTHER WIDGETS* have this setting. Also, there is no RESPONSE — all other widgets have a RESPONSE from admin_ajax.php. WHAT IS GOING ON HERE?

Here is the code:

class Deepwoods_GoogleAdSense extends WP_Widget {
    function __construct() {
      /* Widget settings. */
      $widget_ops = array( 'classname' => 'dwsgoogleadsense',
			   'description' =>
				__('Display Google Ad Sense Blocks',
					'deepwoods') );
      $control_ops = array( 'width' => 300, 'height' => 350,
			    'id_base' => 'deepwoods-adsense');
      /* Create the widget. */
      $this->WP_Widget( 'dwsgoogleadsense',
			   __('Display Google Ad Sense Blocks', 'deepwoods'),
			   $widget_ops, $control_ops );
    }
    /**
     * How to display the widget on the screen.
     */
    function widget( $args, $instance ) {
      extract( $args );
      /* Before widget (defined by themes). */
      echo $before_widget;
      $opts = get_option("deepsoft2_theme_options");
      ?><script type="text/javascript"><!--
		google_ad_client = "<?php echo $opts['google_ad_client']; ?>";
		google_ad_slot = "<?php echo $instance['google_ad_slot']; ?>";
		google_ad_width = <?php echo $instance['google_ad_width']; ?>;
		google_ad_height = <?php echo $instance['google_ad_height']; ?>;
	//-->
	</script>
	<script type="text/javascript"
		src="https://pagead2.googlesyndication.com/pagead/show_ads.js">
	</script><?php
      /* After widget (defined by themes). */
      echo $after_widget;
    }
    static function shortcode ($atts, $content=null, $code="") {
      extract( shortcode_atts ( array(
	'google_ad_slot' => '',
	'google_ad_width' => 0,
	'google_ad_height' => 0), $atts ) );
      $opts = get_option("deepsoft2_theme_options");
      $result  = '<script type="text/javascript"><!--
			google_ad_client = "'.$opts['google_ad_client'].'";
			google_ad_slot = "'.$google_ad_slot.'";
			google_ad_width = '.$google_ad_width.';
			google_ad_height = '.$google_ad_height.';
		//-->
		</script>
		<script type="text/javascript"
			src="https://pagead2.googlesyndication.com/pagead/show_ads.js">
		</script>';
      return $result;
    }
    /**
     * Update the widget settings.
     */
    function update( $new_instance, $old_instance ) {
      $instance = $old_instance;
      $instance['google_ad_slot'] = $new_instance['google_ad_slot'];
      $instance['google_ad_width'] = $new_instance['google_ad_width'];
      $instance['google_ad_height'] = $new_instance['google_ad_height'];
      return $instance;
    }
    /**
     * Displays the widget settings controls on the widget panel.
     * Make use of the get_field_id() and get_field_name() function
     * when creating your form elements. This handles the confusing stuff.
     */
    function form( $instance ) {
      /* Set up some default widget settings. */
      $defaults = array( 'google_ad_slot' => "",
			 'google_ad_width' => 0,
			 'google_ad_height' => 0 );
      $instance = wp_parse_args( (array) $instance, $defaults ); ?>
      <p>
	<label for="<?php echo $this->get_field_id( 'google_ad_slot' );
	?>"><?php _e('Google Ad Slot','deepwoods'); ?></label>
	<input id="<?php echo $this->get_field_id( 'google_ad_slot' ); ?>"
	       value="<?php echo $instance['google_ad_slot']; ?>"
	       name="<?php echo $this->get_field_name( 'google_ad_slot' ); ?>"
	       style="width:100%;" />
      </p>
      <p>
	<label for="<?php echo $this->get_field_id( 'google_ad_width' );
	?>"><?php _e('Google Ad Width','deepwoods'); ?></label>
	<input id="<?php echo $this->get_field_id( 'google_ad_width' ); ?>"
	       value="<?php echo $instance['google_ad_width']; ?>"
	       name="<?php echo $this->get_field_name( 'google_ad_width' ); ?>"
	       style="width:100%;" />
      </p>
      <p>
	<label for="<?php echo $this->get_field_id( 'google_ad_height' );
	?>"><?php _e('Google Ad Height','deepwoods'); ?></label>
	<input id="<?php echo $this->get_field_id( 'google_ad_height' ); ?>"
	       value="<?php echo $instance['google_ad_height']; ?>"
	       name="<?php echo $this->get_field_name( 'google_ad_height' ); ?>"
	       style="width:100%;" />
      </p>
      <?php
    }
  }

  register_widget('Deepwoods_GoogleAdSense');

  add_shortcode('DWS_AdSense',array('Deepwoods_GoogleAdSense','shortcode'));

What am I missing? I have been staring at the code for some time and I am not seeing an error. Maybe a fresh set of eyeballs will spot some silly mistake.