(FORTUNE Magazine) – A constitutional amendment to balance the federal budget was little more than a gleam in the eye of fiscal conservatives a few months ago. Now it's moving through Congress like chicken pox in a kindergarten. The Bush Administration is cheering, and so are some Democrats. One key Senate sponsor is Paul Simon (D-Illinois), a traditional liberal to the tips of his bow tie. His simple amendment would require that the President propose and Congress enact a balanced budget. The last time the budget balanced was 1969, the year Jimi Hendrix played ''The Star-Spangled Banner'' in a meadow near Woodstock, New York. The government has since cranked the volume of borrowing way up, to a total federal debt of nearly $4 trillion. There are reasons to be leery of the balanced-budget push. Congress has shown creative genius in evading previous fiscal rules, such as 1985's Gramm- Rudman-Hollings law. A constitutional amendment, proponents hope, would carry greater force. In addition, the government might be constrained in its efforts to stabilize the economy. But while the idea that fiscal policy could counter booms and busts was popular in the 1960s, it has since fallen from favor. Many economists now think monetary policy the better tool. Besides, the amendment has an escape clause for war or recession. Opposition will come both from tax-and-spend liberals and anything-but-taxes conservatives. Supporters say the amendment may clear Congress by July 4. Then the states would have to ratify it. Let the fireworks begin!