The month of May is likely to bring a bruising battle to Capitol Hill. Congress will vote on raising the debt ceiling, a move that most economists agree would allow the indebted government to continue paying its bills, but Republicans may hold that vote hostage to their own legislative demand for longer-lasting fiscal health, through a balanced budget amendment.

Guided by their belief that the nation is headed for a long-term fiscal calamity, Republicans are promising a fight -- one that may make the battle earlier this spring over government funding resolutions look small in comparison.

Sen. Jim DeMint, R-S.C., vows to "tie the Senate in knots" unless it passes a balanced budget amendment. And while he and Senate Republicans may lack the votes for passage, they wield some leverage -- Democrats need some Republican support to raise the debt ceiling.

Their mutual need leaves room for negotiation. In addition, while Democrats hold a 53 to 47 seat majority in the Senate, they are acutely aware of the changing public sentiment in polls that suggest Americans are becoming deeply concerned with deficit spending and the national debt.

Indeed, a recent NBC News-Wall Street Journal poll found that 61 percent of Americans favor a balanced budget amendment. Only 28 percent disapprove.

Whether those poll numbers can translate into congressional votes remains the subject of dispute. "The national momentum is there for it," said former House Majority Leader Dick Armey, who is now co-chair of the conservative group Freedomworks. "These folks in Congress today, whether they be Republican or Democrat, are acutely aware of the important powerful impact that these big large numbers of swing voters that are so concerned about the national debt, will make in the next election."

But Dan Mitchell of the Cato Institute doubts that the votes are there for a balanced budget amendment.

"There was a test vote in March on a sense of the Senate resolution where 58 senators voted to express support for a balanced budget amendment," Mitchell said. "That's nine votes short, so obviously if I had to bet money, I don't think its going to pass."

Like all constitutional Amendments, a balanced budget amendment would require huge majorities -- two-thirds approval of both houses of Congress, and then ratification by three quarters of the states.

All 47 Senate Republicans have signed a pledge to vote for it, and there are indications that as many as nine or 10 Senate Democrats may be leaning towards yes votes, too.

The last time a balanced budget amendment was introduced in the Senate, in 1997, it failed by just one vote.

Proponents believe the public pressure for such an amendment has grown enormously since those years.

Even so, under the best of circumstances, it could take as long as five years for a balanced budget amendment to become part of the Constitution. Some of the state legislatures that would ratify it meet only once every two years, and debate would likely move at a glacial pace.

Some observers believe a more likely outcome of the Congressional battle that lies ahead is legislation that approximates a balanced budget amendment in the short term by imposing revenue neutrality or some caps on spending.