Sessions added that the Senate has "failed to perform its legal duty," and that according to procedure, it would only take 51 votes to pass a budget, since a filibuster is not allowed on budget votes.

"Unfortunately [the rule] doesn't say the Senate goes to jail for not doing it," Sessions said.

He also accused Senate Democrats of failing to come up with a fiscal vision for the country, and said if Republicans regain control of the Senate, they will pass a budget.

Johnson said the budget put forward by President Obama was not serious, as evidenced by the unanimous vote against it. "Not one member of his own party voted for it," Johnson said.

Senate Budget Committee Chairman Kent Conrad (D-N.D.) has hinted that he would propose a vote on the Bowles-Simpson fiscal commission budget plan during the lame-duck session after the elections.