This is of course, completely and totally false. One only needs to look at the stats to see that, depending on circuit, they end up with something like 3 new appeals per day on the low side, and 40 new appeals per day on the high side.
http://www.uscourts.gov/Viewer.aspx?doc=/uscourts/Statistics...
Given the amount of time and effort it takes to decide a single appeal, the caseload is not "light" by any stretch of the imagination.
Pendency is huge (even though very slowly decreasing on average)
These stats also don't count the time it actually takes to hear argument on cases, etc. Just the number of filings.
Truly inappropriate nominations (ie, Harriet Myers) can still be blocked by majority vote.
The entire filibuster was never laid out in the constitution, it's a convention adopted by the Senate itself and was used ruthlessly by southern racist senators (both Dem and GOP) to block progressive legislation despite being popular and wanted by the majority.
[1]: http://www.senate.gov/artandhistory/history/common/briefing/...
In my opinion, it was right for the Senate to give up a little power here. They should be exercising more oversight powers in other areas.