McConnell wants to wrap up immigration debate this week

Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellPelosi: Congress will receive election security briefing in July Adam Scott calls on McConnell to take down 'Parks & Rec' gif Trump says he spoke to Pelosi, McConnell on border package MORE (R-Ky.) is signaling he will move to wrap up the Senate's immigration bill this week, warning senators against slow-walking the debate.

"Senators have had plenty of time to prepare. There's no reason why we should not reach a bipartisan solution this week," McConnell said from the Senate floor.

He added that he made a commitment to hold an immigration debate "this week."

"I've lived up to my commitment. I hope everyone will cooperate so this opportunity does not go to waste," he said.

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McConnell's comments are the clearest indication yet that the GOP leader does not intend to let the immigration fight linger over the upcoming weeklong Presidents Day recess.

In a deal to end the three-day government shutdown in January, McConnell promised to turn to the immigration debate after Feb. 8. His public remarks did not include a time limit for how long he would keep a bill on the floor.

The push to wrap up the debate this week comes as senators are struggling to find an immigration proposal that could win the 60 votes needed to overcome a likely filibuster.

Republican senators had predicted that the Senate's free-wheeling debate could last weeks. But Sen. John CornynJohn CornynSenate passes .5 billion border bill, setting up fight with House 2020 debates complicate Senate plans for vote on Trump's war authority Senate GOP to defeat proposal requiring approval for Iran attack MORE (R-Texas) appeared to pivot on Monday evening, saying senators had until Thursday.

Responding to a top staffer for Sen. Dick DurbinRichard (Dick) Joseph DurbinDemocrats leery of Sanders plan to cancel student loan debt McConnell opens door to vote on Iran war authorization Negotiators face major obstacles to meeting July border deadline MORE (D-Ill.) on Tuesday, Cornyn noted the agreement only included a start date and a "fair an [sic] open process."

"Delivered as promised. Clock is ticking so I am anxious to see D counteroffer to POTUS’s proposal that can become law. None so far," Cornyn said in a tweet.

With the Senate expected to be out of town next week, debating the issue for two weeks could have pushed the chamber's final vote up against the initial March 5 deadline to find a fix for the Deferred Action for Childhood Arrivals (DACA) program.

McConnell is backing a GOP plan, spearheaded by Sen. Chuck GrassleyCharles (Chuck) Ernest GrassleyThe Hill's Morning Report - Democratic debates: Miami nice or spice? Senate Finance leaders in talks on deal to limit drug price increases Million-dollar drugs pose new challenge for Congress MORE (R-Iowa), that largely mirrors the White House's proposed framework.

Updated at 11:06 a.m.