It comes from the procedural rules of the Senate Judiciary Committee (where the eventual nominee will first be considered) and it defines how matters before the panel are put to a vote. Rule IV:
The Chairman shall entertain a non-debatable motion to bring a matter before the Committee to a vote. If there is objection to bring the matter to a vote without further debate, a roll call vote of the Committee shall be taken, and debate shall be terminated if the motion to bring the matter to a vote without further debate passes with ten votes in the affirmative, one of which must be cast by the minority.
Back in the heady days of last week, that one vote might have belonged to Arlen Specter. Now it will have to come from within the ranks of a several more conservative senators, who, in order of seniority are Orrin Hatch (R-UT), Chuck Grassley (R-IA), Jon Kyl (R-TX), Jeff Sessions (R-AL), Lindsey Graham (R-SC), John Cornyn (R-TX), Tom Coburn (R-OK), and, potentially, a Republican to be named later.
The Senate is thick with choke points and this is just one of them. That doesn't mean the Republicans will necessarily go in for it--Graham, for instance, is one of the Gang of 14 opponents of the judicial filibuster. But the idea is already making its way through the political and legal blogosphere. So it's certainly not out of the question.