The revised Budget Control Act would cut the deficit by $917 billion over 10 years, and cut $22 billion in 2012. It also increases the debt ceiling by $900 billion, and sets out a process by which Congress must look for another $1.8 trillion in cuts over the next decade and move on that plan by the end of the year.

The bill also requires a vote on a balanced budget amendment to the Constitution, and the rule approved Wednesday evening by the committee anticipates a vote on a balanced budget amendment in the next few days under a suspension of House rules. House staffers said a vote on the balanced budget amendment is "likely" on Friday.

A suspension vote means passage would require support from two-thirds of voting members.

Current House rules require suspension votes to be held on Monday, Tuesday or Wednesday. However, the rule provides "suspension authority" through this Sunday, which means the balanced budget amendment could come up under a suspension of the rules anytime through July 31.

If the amendment vote does come up, the rule allows for two hours of debate, which is longer than the time normally allowed for suspension votes.