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Two Republicans — Sen. Lindsey Graham of South Carolina and Minority Leader Mitch McConnell of Kentucky — appeared so eager to revive the bill they initially voted the wrong way on a previous labor union rights vote, before catching themselves and switching.

Even if the bill survives the Senate this week, the House may be a bigger challenge for Mr. Bush, who faces a full-scale revolt in his own party on the issue.

House Republicans voted 114-23 yesterday to pass a resolution disapproving of the Senate bill, a stark move that sends a signal to Mr. Bush, House Democrats and Senate Republicans.

House Minority Leader John A. Boehner, Ohio Republican, said he gave a “heads-up” to the White House that the vote was coming and “they weren’t happy about it.”

But Republicans said they needed to make a statement to distance themselves from the bill, which they fear could be labeled a “Republican” bill because of the support of Mr. Bush and Senate Republicans.

“This is not a Republican bill. The House Republicans don’t want to be associated with this bill, and are opposed to it,” said Rep. Peter T. King, New York Republican.

In the Senate, some Republicans fear the same thing.

Sen. Jim DeMint of South Carolina said Tuesday’s parliamentary maneuvering proves this bill belongs to Mr. Reid.

“He used his power as majority leader to manipulate and abuse the rules of the Senate to ram this bill down our throats,” Mr. DeMint said.

Mr. Reid, though, said Mr. Bush and Mr. McConnell agreed to the tactic, which he said has been used before.

“I would not have considered employing it in this instance without the full support of Senator McConnell,” Mr. Reid wrote in a letter earlier this week, adding, “the White House made clear that it also favors such a procedure, since the immigration bill is one of President Bush’s top priorities.”

c S.A. Miller contributed to this report.