But Republicans also argue that the administration is unfairly exempting companies from a critical element of ObamaCare, while forcing everyday Americans to comply with the requirement to buy health insurance. Republicans will now vote on another bill that would delay the individual health insurance mandate for a year.

On Tuesday, House Speaker John BoehnerJohn Andrew BoehnerWe need more congressional oversight on matters of war A warning to Ryan’s successor: The Speakership is no cakewalk With Ryan out, let’s blow up the process for selecting the next Speaker MORE (R-Ohio) made a rare floor speech where he said that it's unfair of the Obama administration to give companies an exemption from the law that it is unwilling to give to individuals.

While the first bill simply mirrors the Obama administration's exemption for companies, the administration has said it would veto the bill if it were presented for the president's signature. The White House called it "unnecessary," and said the bill delaying the individual health insurance mandate would "raise health insurance premiums and increase the number of uninsured Americans."

By the end of the day, the House will likely pass both bills, and send them to a Senate that will ignore them.

The Senate starts at 9:30 a.m., and at 10 a.m. will hold a vote to end debate on the nomination of Fred Hochberg to be president of the Export-Import Bank. The Senate may be in a position to approve Hochberg later in the day.

Those votes should be easy, in light of Tuesday's agreement by both parties to back away from a war over Senate procedures. Democrats angry with Republican filibusters had threatened to end the filibuster for Executive Branch nominations, prompting Republicans to argue that this course would fundamentally alter the Senate and increase political tensions in the upper chamber.

Under Tuesday's deal, senators agreed to approve the nomination of Richard Cordray to be director of the Consumer Financial Protection Bureau, and Democrats scrapped two controversial appointees to the National Labor Relations Board.