Senate Minority Leader Mitch McConnell, R-Ky., may be open to final passage of the $1 trillion bipartisan infrastructure deal, but he warned Majority Leader Chuck Schumer, D-N.Y., not to try to cut off debate early.
Such a move might just kill the deal altogether, McConnell said.
"The best way to pass this infrastructure bill is not to file cloture today and speed the process," McConnell told reporters on Tuesday. "If the majority leader files cloture today I'll be encouraging my colleagues, including the negotiators, not to invoke cloture on Thursday."
Cloture is the process of winding down debate.
"This is an extremely important bipartisan bill. There's an excellent chance that it will be a bipartisan success story for the country," added McConnell, who was one of 17 Republicans who have helped push the bill.
Senators "must work efficiently," Schumer told reporters, in his daily press conference, while McConnell countered, "My best advice to the majority leader would be slow but steady wins the race."
The Hill quoted a Senate Democratic aide as saying he had never heard Schumer say he had any intention of cutting off debate on Tuesday, and Sen. Dick Durbin, D-Ill., said he had heard nothing of such a move by Democrats either when asked about it.
But multiple Republicans have been concerned that Schumer intends to stop debate Tuesday in order to set up a vote on Thursday. When the language of the bill was released on Sunday night, it was presented as likely to receive passage in the Senate this week.
Should the Thursday vote scenario play out, Schumer would need 10 GOP votes for passage, and Republicans would be allowed to block an end to debate.
"If he files tonight, there will be an effort to get 41 of us to deny cloture," said Sen. John Cornyn, R-Texas.
Most Republicans oppose the bill because of the inclusion of what have been called non-traditional infrastructure as well as the cost. But they want a chance to amend the bill as much as possible since they see passage as inevitable.
About 175 amendments had been filed as of Tuesday morning. As of Tuesday afternoon, three minor amendments had been approved and two rejected. It was not known how many more amendments would be proposed.
Sen. John Thune, R-S.D., and the No. 2 Republican in the Senate suggested ending debate on Thursday and voting on the bill on Saturday.
Either way, senators were unlikely to be able to start their summer recess next week as scheduled given that Schumer has vowed to debate a budget resolution laying out plans for a $3.5 trillion "human infrastructure" bill immediately after passage of the $1 trillion bill.
That larger effort is not expected to win support from Republicans, many of whom oppose its major initiatives, including money to address climate change, funding to expand home healthcare for the elderly and protections for some illegal immigrants.
Senator Mike Rounds, R-S.D., told reporters that one of the challenges for the $1 trillion bipartisan bill was "poison pill" amendments that, if approved, could potentially unravel the delicately-negotiated measure.
Highlights of the legislation include $550 billion in new spending over five years for items such as roads, rail, electric vehicle charging stations and replacing lead water pipes on top of $450 billion in previously approved funds.
The legislation would be the largest U.S. infrastructure investment in decades. If passed by the Senate, the House of Representatives would not debate it until sometime this autumn.
The conservative group Heritage Action for America on Tuesday urged senators to vote against the legislation, saying it "recklessly spends $1 trillion."
Reuters contributed to this report.
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