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 Mason ReidWATCH: There is no Trump-Russia collusion and the media should stop pushing this The demise of debate in Congress ‘North by Northwest,’ the Carter Page remake 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 GrassleyCharles (Chuck) Ernest GrassleyPavlich: The claim Trump let the mentally ill get guns is a lie Congress fails miserably: For Asian-Americans, immigration proposals are personal attacks Grassley, Dems step up battle over judicial nominees 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.