Many Republican senators dismissed the idea of overruling the Senate parliamentarian after she rejected key Medicaid provisions in Trump's tax and immigration bill Thursday, which dealt a blow to Republicans' plan to slash costs in the budget package.

The reconciliation process lets Republicans push the bill through the Senate—where they have a 53-47 majority—on a simple majority vote. But the process comes with strings attached, and those limits are known as the Byrd Rule, for the late Sen. Robert Byrd (D., W.Va.).