The rule also covers H.R. 2576, which would "pay for" the repeal by changing the way modified adjusted gross income (MAGI) is calculated under last year's healthcare law. Republicans say the healthcare law makes it too easy for middle-income Americans to qualify for Medicaid and other health programs, which would raise the cost of these programs and defeat the point of these programs, which is to help lower-income Americans.

A few House Democrats argued against this offset today, but their arguments were undercut by other House Democrats, and the Tuesday announcement that the Obama administration supports both bills.

H.R. 2576 is estimated to save $13 billion, and the Congressional Budget Office said late Wednesday that the cost of repealing the withholding rule is $11.2 billion.

House passage of the rule should allow members to approve the bill by Thursday.