With their leader conspicuously absent from the floor debate on immigration, a small band of Senate GOP conservatives successfully fought Majority Leader Harry Reid (D-Nev.) to a draw Wednesday night, using the restrictive rules Reid and Minority Leader Mitch McConnell (R-Ky.) imposed on the debate to ultimately bring it to the verge of collapse.

Following a day of parliamentary guerrilla warfare that slowed consideration of the bill, GOP Sens. Jim DeMint (S.C.), David Vitter (La.), Tom Coburn (Okla.) and Jeff Sessions (Ala.) pulled off what could end up being the death blow to the immigration debate when they voted for a Democratic amendment and then objected to further proceedings — stalling work on the measure and crippling chances it will eventually pass.

Under an agreement between Reid and McConnell, Reid has used an obscure parliamentary procedure known as the clay pigeon to maintain a tight grip on the Senate floor to block efforts by conservatives to introduce amendments that would undermine the underlying agreement behind the bill.

Until late in the day Wednesday, supporters of the bill had, as expected, blocked a series of amendments. But during the chamber’s vote on a real ID proposal backed by Montana’s Democratic Sens. Max Baucus and Jon Tester, conservatives realized it had strong enough support among Democrats that if they voted for the measure, it could hang the bill.

Because of the restrictive rules of the clay pigeon tactic, if an amendment within the pigeon is not defeated, Reid must get unanimous consent to move to a new amendment — a request to which conservatives objected.

Additionally, the delicate nature of the agreement to move the bill, including the Baucus-Tester amendment, throws the likelihood that Reid can invoke cloture on the bill today into serious doubt, since it appears enough Republicans oppose the amendment to block cloture.

However, while under the clay pigeon Reid could in theory simply remove the language, that could severely shake lawmakers’ faith in the process and likely doom the cloture vote as well.

Although Members of both parties were initially wary of using such heavy-handed tactics to move the bill, McConnell and Reid promised their Members that a series of votes would be held prior to today’s 9 a.m. cloture motion to build Members’ confidence in the process.

But with McConnell off the floor for virtually the entire day save the amount of time it took him to cast a handful of votes, a group of Republican conservatives essentially derailed that agreement by objecting to any debate on amendments and dragging out the voting process through simple objections.

Vitter and DeMint took turns throughout the day opposing proposed debate limits unless they were given the floor without restrictions — a demand Reid repeatedly denied.

As a result, the debate quickly broke down into a series of back and forths between conservatives and Reid over their inability to offer amendments, followed by long votes on different provisions of the clay pigeon.

The breakdown in the agreement clearly frustrated many lawmakers, including Finance ranking member Chuck Grassley (R-Iowa). “It doesn’t do much good to make a promise to me to offer an amendment if I don’t have a chance to debate my amendment,” he said angrily on the floor Wednesday.

But Reid spokesman Jim Manley argued that Republicans had undercut a deal with McConnell to allow voting to proceed.

“We worked out an agreement with Sen. McConnell to get a number of votes through before cloture to build confidence [in] the process. Unfortunately, the Republicans wouldn’t let us do that,” Manley said.

The absence of McConnell — arguably the GOP’s best floor procedural strategist in addition to being the party’s Senate leader —raised eyebrows in the chamber, particularly as the stand-off between Reid and the conservatives began to wear nerves thin.

Sen. John Thune (R-S.D.) sympathized with McConnell, arguing that he finds himself in a difficult position on immigration, with the White House and business interests on one side pushing for the measure, while on the other, conservatives and many of his own constituents — as well as McConnell himself — oppose the legislation. “I don’t think he agrees with the bill,” Thune said.

McConnell also is under increasing fire in Kentucky from both sides of the immigration debate. Talk radio hosts and conservative Web sites have become increasingly frustrated with the agreement he made with Reid to return to the issue. At the same time backers of the measure — including the Louisville Courier-Journal editorial board — have pushed McConnell to ensure that some sort of immigration reform is passed this year.