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Paul, making the case for his bill ahead of the vote, warned that Congress will face a "day of reckoning" without changes to the country’s spending habits.

"If we keep piling on the debt we’re going to come to a day of reckoning. We have a great country and we shouldn’t let it get away from us," Paul wrote on Twitter on Monday.

Paul got the support of GOP-aligned outside groups, which lobbied lawmakers ahead of Monday’s vote to back the proposal. FreedomWorks argued that “any responsible Republican” would support the legislation, while Club for Growth warned that it would “key vote” the measure.

“Congress needs to operate its budget like American families operate their budget. That means cutting up the credit card and ending excessive annual deficits that balloon the national debt,” the group said in a statement.

But the proposal was expected to fail after the Senate rejected a similar measure along bipartisan lines last year.

The vote comes as top members of congressional leadership and the White House are trying to work out a deal to lift budget caps on defense and nondefense spending by Oct. 1 to prevent across-the-board budget cuts known as sequestration.

—Updated June 4 at 4:25 p.m.