Black has pointed out that today, the budget resolution is just between the House and the Senate, when it happens at all. The Senate has not approved a budget in nearly three years.

"Requiring a joint resolution would encourage agreement between the House, Senate and the president on the budget at the beginning of the budget process," Black wrote in a "Dear Colleague" letter.

After a rule is approved for the bill Monday, the bill is expected to be the subject of a hearing in the House Budget Committee on Wednesday.

— This story was updated at 12:49 p.m. to correct information on how the bill will move through the two committees next week.