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Senate Majority Leader Harry Reid, Nevada Democrat, announced this year that he will try to force a rules change in January to limit the number of chances to filibuster a bill — though he would not eliminate it entirely.

Minority Leader Mitch McConnell, Kentucky Republican, vehemently objected, and the two have sparred repeatedly on the chamber floor.

Mr. McConnell objects not only to the rules change, but also the way Mr. Reid plans to go about it.

The Democrat wants to use the first day of the next session, when the chamber adopts its entire rules package on a majority vote, to do the rewrite. Though that would be legal, most major rules changes are passed by a two-thirds vote, which ensures widespread support.

Both Mr. Reid and Mr. McConnell signaled they would be open to sitting down and talking about a compromise, though it’s not clear what middle ground can be found.

Last year, the two men struck a gentleman’s agreement that Mr. McConnell would allow more bills to come to the floor without an initial blockade, and in exchange Mr. Reid would allow Republicans to offer amendments. That deal soon collapsed, however, with each side blaming the other for its demise.