Reid and McConnell have been negotiating to make the Senate more efficient by limiting filibusters and allowing more amendment votes. Reid said Tuesday that he would hold a vote to change the rules by the end of the week. He has been delaying the first day of Congress by recessing instead of adjourning so that a simple majority can still vote to change the rules, rather than the 67-member supermajority vote normally needed.

“We’re not going to get everything we want, but maybe we can find a sweet spot in the middle to make the Senate more efficient,” Reid said. “There must be some agreement reached or we’ll have to use other means to make the Senate more efficient.”

Democrats have called for limiting the minority party’s right to filibuster a motion to proceed and go to conference with the House, but negotiations are still under way.

During Tuesday lunches, both leaders outlined prospective rule changes for their caucuses to assess the support they would receive.

Reid said he believes he has enough votes for simple-majority passage of rule changes within his party alone, but would prefer to come up with an agreement that both sides can agree on.