So I was completely out of the loop on the Google Feed API being terminated.
Today has been all about writing a quick replacement, and implementing it on a dozen+ websites. The scripts below were written to replace the API for three examples: a Blogger JSON feed, a JSON feed from a Google Drive spreadsheet, and a JSON feed from Picasa. In the spreadsheet examples the field names are generated by the first row in the spreadsheet.
Enjoy, and I hope this helps!
// blogger feed example
// : title, url, date, media thumbnail
var url = 'http://www.confluentforms.com/feeds/posts/default?alt=json';
$.getJSON(
  url + '&callback=?').
  done(function(data){
    $.each(
      data.feed.entry || [],
      function(i, e){
 var title = (e.title.$t || '');
 var url = (e.link || []).pop().href;
 var date = new Date(e.updated.$t || Date.now());
 var thumbnail = (e.media$thumbnail.url || ''); 
 // do your stuff here
      });
  }).
  fail(function(){
    // handle failure here
  });
// google spreadsheet example
// : location, photo, logo, url, title, showcase, number, category
var url2 = 'https://spreadsheets.google.com/feeds/list/0AuaRGq3RzJsadFdMUHhPNC1WQ3hrNkdTaGYzbzZLTWc/od6/public/basic?alt=json';
$.getJSON(
  url2 + '&callback=?').
  done(function(data){
    $.each(
      data.feed.entry || [],
      function(i, e){
 var entry = {};
 $.each(
   e.content.$t.split(','),
   function(i, x){
     var s = x.split(':');
     var key = s.shift().trim();
     entry[key] = s.join(':').trim();
   });
 
 // do stuff here, entry has column headers as keys
 
      });
  }).
  fail(function(){
    // handle failure here
  });
// picasa feed example
var slides = new Array();
var captions = new Array();
var url3 = 'http://picasaweb.google.com/data/feed/api/user/106704368739672674589/albumid/6184901565410700577?kind=photo&imgmax=800&alt=json';
$.getJSON(
  url3 + '&callback=?').
  done(function(data){
    $.each(
      data.feed.entry || [],
      function(i, e){
 var entry = {};
 $.each(
  slides[i] = entry.content.src;
  captions[i] = entry.summary.$t;
   );
 
      });
  }).
  fail(function(){
    // handle failure here
  });
If you need help finding your User ID or Album ID for Google Photos please read this.
The following is an example feed grab that you can place into a HTML widget
<ul id='newsandevents'></ul><br /><div style='display: block; clear: both;'><a href="/search/label/news%2Bevents?max-results=100" class="morenews">more news & events</a></div><script type='text/javascript'>//<![CDATA[
var imageReg = /s\B\d{2,3}-c/;
$(document).ready(function(){
 var slideContainer = $('#newsandevents');
 var url = 'http://www.pinchgallery.com/feeds/posts/default?alt=json';
 $.getJSON(
   url + '&callback=?').
   done(function(data){
  $.each(
    data.feed.entry || [],
    function(i, e){
   if(i<3){
    var title = (e.title.$t || '');
    var content = (e.content.$t || '');
    var url = (e.link || []).pop().href;
    var date = new Date(e.updated.$t || Date.now());
    date = (new Date(date)).toLocaleDateString(
     'en-us',{
      month: 'long',
      day: 'numeric',
      year: 'numeric'
     }
    );
    var thumbnail = (e.media$thumbnail.url || ''); 
    var thumbnail = thumbnail.replace(imageReg,'s80-c');
    var slideEntry = document.createElement("li");   
    var slideContent = "<a href='" + url + "' class='newstitle'><img src='" + thumbnail + "' style='float: left; padding-right: 10px; padding-bottom: 5px;'/>" + title + "</a>";
    slideEntry.innerHTML=slideContent;
    slideContainer.append(slideEntry);
   }
   
    });
   }).
   fail(function(){
  // handle failure here
   });
});
//]]></script>