Here’s the WaPo story on the 56-34 vote in the Senate, which failed to invoke cloture in order to proceed to a vote on the House measure. Seven Republicans voted to invoke cloture, despite the refusal of Senate Democrats to permit a vote on another measure pledging not to cut off funding for the troops:

The seven Republican senators who broke ranks with their colleagues and voted in favor of the cloture motion were John W. Warner (Va.), Chuck Hagel (Neb.), Norm Coleman (Minn.), Gordon Smith (Ore.), Olympia Snowe (Me.), Arlen Specter (Pa.) and Susan M. Collins (Me.).

No surprises there. I couldn’t find out how Lieberman voted.

Update: The NYT story contains this nugget:

Republicans continued to try to make the case that it was Democrats who were shutting down a full-fledged Senate review of Mr. Bush’s Iraq strategy by refusing the Republicans a chance to offer an alternative that would place the Senate on record against cutting off money for armed forces in the field.

“This is the United States Senate,” said Senator Jim Bunning, Republican of Kentucky, defending his party’s stance as senators squared off at noon. “The majority cannot tell the minority what we are going to have one vote on, take it or leave it.”

Democrats were leery of the Republican plan, written by Senator Judd Gregg of New Hampshire, because of its potential to attract the most Senate votes and to overshadow Senate action criticizing the troop increase. Some lawmakers also believed that Congress might be asked to restrict military spending, and they did not want their hands tied by an earlier vote on a more symbolic resolution.

Update #2: Power Line informs us the Lieberman voted against cloture.