The Senate will not vote on any more immigration amendments this week, but will have a heavy slog beginning Monday, Senate Majority Leader Harry ReidHarry ReidOPINION | 5 ways Democrats can win back power in the states THE MEMO: Trump's base cheers attacks on McConnell It's time for McConnell to fight with Trump instead of against him MORE (D-Nev.) told the chamber. 

Reid on Thursday also said the Senate could work on amendments to the bill next weekend, a threat the majority leader frequently makes but usually does not follow through on.

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“We’re going to finish the work on the floor here soon, but we’re going to come back Monday and be on this bill,” Reid said. “Next weekend we will be working on this bill. We will finish this bill before the July recess.”

Senate leaders were working on an agreement to vote on at least four more amendments Thursday, but Reid said because of a storm approaching Washington, D.C., the Senate would continue work on those amendments next week.

He spoke after the Senate voted to table Sen. Chuck GrassleyChuck GrassleyWhite House clarifies: We condemn all violence Republican lawmakers criticize Trump response to Charlottesville Grassley reverses ‘expectation’ of Supreme Court vacancy this year MORE's (R-Iowa) amendment, which would have required the border to be secure for six months before immigrants in the country illegally would have been provided with a pathway to citizenship.

The Senate began considering the immigration reform bill this week. Work on amendments is expected through the end of the month.