Even more temperate Republican voices like Senator John Cornyn of Texas, who had encouraged the negotiations, said that after reviewing it, he harbored “serious concerns.” (Mr. Cornyn, who is often mentioned as a potential successor to Mr. McConnell as the Republican leader, notably gave the statement to the hard-right news outlet Breitbart.)
It pointed to a bleak outlook for the complicated compromise bill that followed a longstanding pattern on Capitol Hill, where major immigration agreements have often come close to enactment only to fall apart just before the finish line after Republicans condemn them as too weak.
The first test for the measure will come on Wednesday, when an initial procedural vote is planned. It needs 60 votes to advance, meaning at least 10 Republicans would have to back it. Even if the bill scales that hurdle and could pass the Senate, there appears to be no path forward in the House.
“The $64,000 question now is whether or not senators can drown out the outside noise, drown out people like Donald Trump who want chaos and do the right thing for America,” Senator Chuck Schumer, the majority leader, said in a speech on the Senate floor on Monday afternoon. “I urge senators of good will on both sides of the aisle to do the right thing and tune the chaos out.”
Mr. Schumer reminded his colleagues that “we live in an era of divided government, and that means that both sides need to compromise if we want to pass a bill.”