The Senate debate over the immigration compromise bill was showing signs of trouble Tuesday as leaders began shifting blame to opposing sides on problems that had yet to be resolved.

Sparking the spat was Senate Majority Leader Harry Reid's expected use Tuesday of a procedural motion available only to Democrats that would shut off debate on the comprehensive immigration bill. But Republicans say that move could very well kill the bill. Reid's move would come up for a vote Thursday.

Senate Minority Leader Mitch McConnell, R-Ky., told reporters that Republicans will stand united against Reid if Democrats block consideration of an unspecified number of Republican amendments. Reid would need 60 votes to shut off debate, but he would fail if Republicans hang together.

Sen. Jon Kyl, a key negotiator in the immigration reform process, said he would be disappointed if Reid, D-Nev., made such a move.

"That would be extraordinarily disappointing, an extraordinary act of bad faith," Kyl, R-Nev., said. "Cutting off members rights on something so complex, so emotional, so controversial, would be an act that a true leader would want to avoid. ... I would hope cooler heads would prevail."

Generally, once this sort of heated debate breaks down into finger pointing, a bill's chances of survival are grim. But Reid has left one escape route: He has asked for each side to put forward their respective lists of amendments that are directly related to this bill, signaling a possible compromise. But the deal is on the table only if enough Republicans would support Reid's motion.

"Let's see if they can come up with a list of germane amendments. We'll take a look at that," Reid told reporters.

The in-fighting has had its effect on voter perspectives, McConnell argued. He cited a poll out Tuesday that shows Americans are not pleased with the performance of the Democratically-led Congress. Reid countered that "polls also show that Republican members are not as well thought of as Democrats."

The negotiators who put together the compromise are feverishly working to smooth this over and save the bill, but the outcome is uncertain. Republican leadership aides tell FOX News they think a deal ultimately will be worked out, possibly just before Thursday's vote.

The Senate, counting Tuesday's votes, has considered nine amendments by roll call in just four days of debate. A number of voice votes on less controversial amendments have also occurred. Last year, the Senate considered more than 30 amendments. This time around, Reid said that just goes to show there is less of a need to have as many amendments.