The Byrd Rule, adopted in 1985, is a procedural constraint named after the late Senator Robert C. Byrd of West Virginia to prohibit “extraneous” provisions from being tacked onto reconciliation bills, which are fast-tracked budget packages that allow legislation to pass with a simple majority, bypassing the 60-vote filibuster threshold.

Senate Parliamentarian Elizabeth MacDonough dealt big-time blows to GOP priorities this weekend when she ruled that chunks of President Trump's "big, beautiful bill" violate the chamber's rules.

Majority Leader John Thune's comments are a sign of the growing pressure he faces to get Republican hold-outs on board.