The Constitution already places strict limits on what the federal government can and cannot do. The problem is that those limits have become stretched over the years to the point that the federal government can do pretty much what it pleases. As a result, Americans have become accustomed to, and dependent upon, the federal government to supervise their lives from cradle to grave.
Most Republicans are about as enthusiastic to confront this reality as most Democrats are in reversing it. Thus, the convenient resurgence in popularity for a balanced budget amendment on the part of Republicans has been driven by an unwillingness — or inability — to flesh out exactly what federal agencies and programs would have to go in order to bring the budget into balance without raising taxes.
Indeed, it's not a coincidence that the balanced budget amendment wasn't a priority for Republicans when they were jacking up spending and debt during George W. Bush's tenure. Now that the Obama Democrats have done the Republicans one better on the fiscal profligacy front, the GOP is really just looking to score political points for the November 2012 elections by hoisting up the balanced budget amendment as a litmus test for fiscal propriety.