The plans, which Democrats say would balance the budget by 2012, include pay-as-you-go rules prohibiting new tax cuts and new spending if they would increase the deficit, The Washington Post reported.
The national debt is $8.8 trillion, or about $29,000 for every person in the country, the Congressional Budget Office said.
Republicans say the rules the Democrats propose would force U.S. President George W. Bush's tax cuts to expire in 2010 and require the biggest tax increase in U.S. history.
But passing a credible budget would enhance the Democrats' stature for next year's elections, strategists from both parties say.
"If they can at least tout that they've got a balanced budget put together, then I think they undermine the Republicans and set themselves up well to claim the mantle of fiscal responsibility going into 2008," former top Republican aide G. William Hoagland told the Post.