Democrats, for a second time on Tuesday , blocked Republicans from holding initial votes on immigration plans.

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"There have been meetings that have been going on all day on a bipartisan basis to try to resolve the issue before us. ... I believe progress is being made. I hope that we can continue along those lines," he said.

McConnell and other GOP senators hammered Democrats throughout Tuesday for slow-walking the immigration debate after demanding that it be brought to the Senate floor as part of the deal to end a three-day government shutdown in January.

Senators had predicted that they would have a wide-ranging free-for-all of a debate this week as they hunt for a plan that can get 60 votes, the amount needed to break a filibuster. Instead, the rhetoric took an increasingly partisan turn on Tuesday with both sides arguing the other needed to compromise to move the chamber forward.

As a result of the standstill, the Senate is expected to vote to formally begin debate on Wednesday morning.

GOP senators said McConnell collected signatures for cloture petitions during a closed-door caucus lunch earlier Tuesday as he looks for a way to break the current logjam.

The GOP leader wants to wrap up debate on the immigration bill by the end of the week.

“We have other things to do,” he told reporters, when asked if he would let the debate extend beyond this week.