A Republican congressman on Tuesday pressured leadership to hold a clean vote on raising the debt ceiling in order to show Democrats it cannot pass the House. 

Rep. Jason Chaffetz (R-Utah), an outspoken second-term lawmaker, said that such a vote would fail but that House GOP leaders should hold it anyway, saying it could divide Democrats and drive home the GOP's argument that spending reforms need to be attached to a vote to raise the debt limit.

"In fact, I would encourage the Speaker to take a straight up-or-down vote," he said on Fox News.

The debate surrounding the nation's $14.3 trillion borrowing limit is heating up. The U.S. officially reached its limit on Monday, starting a countdown clock to Aug. 2, when Treasury Secretary Timothy Geithner says the country will actually default on its debt. 

But both sides remain far apart on a deal to raise the limit: Republicans and Democratic leaders are negotiating but disagree on spending and budget reforms that could potentially be attached to a vote on the debt ceiling. 

Chaffetz's plan could allow Republican leaders to underscore their point about spending cuts to the White House and Democrat leaders in Congress.

"There are many of my Democratic colleagues ... who just want to unilaterally raise the debt ceiling by, say, $2 trillion," he said. "Well, my encouragement to Speaker [John] Boehner [R-Ohio] is, 'go ahead, let's have that vote' because I don't think it will pass. I think it will be bipartisan, I think it will be knocked back down.

"We have to take this opportunity in time to make the major systemic changes to put us on a pathway to balance the budget."

Senate Democrats are using a similar tactic to illustrate the lack of support in the upper chamber for Rep. Paul Ryan's (R-Wis.) budget plan. Majority Leader Harry Reid (D-Nev.) said that he will hold a vote on it, which he says could divide Republicans.

The office of House Majority Leader Eric Cantor (R-Va.), who controls the calendar, said the idea of holding a vote to raise the debt ceiling without spending cuts is under consideration.

"It's an option being considered," Cantor spokesman Brad Dayspring said.