The following is a fact-check of the May 16, 2010 episode of Meet the Press:

SEN. MITCH McCONNELL (R-KY) | Pres. Obama, VP Biden, Sen. Harry Reid, & Sen. Patrick Leahy filibustered the S.C. nomination of Sam AlitoTRUE

SEN. McCONNELL: the way Sam Alito was, who was filibustered by the president, the vice president, the Democratic leader and the chairman of the ranking member of the Judiciary Committee. I’ve never filibustered a Supreme Court nomination.

From crowd-sourcer James:

In 2006, Senator John Kerry along with Obama, Biden, Reid and Leahy (at the time the ranking member of the Judiciary) did mount a brief but unsucessful filibuster of Alito’s nomination. Here is the link to the cloture vote:
U.S. Senate: Legislation & Records Home > Votes > Roll Call Vote

Page 2 of this pdf by the Congressional Research Service has detailed information and history on cloture attempts on nominations.

James’ research and conclusion is sound. Senator McConnell’s statement gets a TRUE.

This fact-check took a combined 20 minutes.