Seeking more public support for their budget-cutting plans, congressional Republicans are trying to force the opposition to show its cards.

The House on Wednesday passed a bill authored by Republican U.S. Rep. Tom Price of Roswell that would mandate the president offer details on whether and when his proposed future budgets come into balance.

Washington’s serial fiscal strife will continue in the coming weeks when the president offers his yearly budget, along with House Republicans and Senate Democrats. House leaders have said their budget will break even within 10 years. The Senate has gone four years without passing a budget, deferring to a fiscal commission and then negotiated short-term spending agreements.

The nonpartisan Congressional Budget Office said Tuesday that the fiscal 2013 budget deficit will be $845 billion — the first time in five years that the nation will run a deficit under $1 trillion.

Recent Republican budgets have sought significant cuts to some domestic programs while converting the Medicare health program for seniors into a voucherlike system for future beneficiaries and the Medicaid health program for the poor into a block grant to states. Democrats have aggressively attacked those plans as shredding the social safety net. They have not proposed structural changes to those health programs — which carry big costs in the long run for an aging nation.

“It’s huge because the other side can demagogue possible solutions we put on the table without having to defend anything because they haven’t put anything on the table,” said Price, the second-ranking Republican on the House Budget Committee behind U.S. Rep. Paul Ryan of Wisconsin. “… When we get the facts out there and a true contrasting of visions, we think the support of the American people will follow.”

Democrats have extracted savings from Medicare — and taken GOP criticism for it — in the Affordable Care Act, and President Barack Obama has proposed further measures to reduce long-term Medicare costs. But he has not put forward a specific path to balance the budget.

On the House floor U.S. Rep. Chris Van Hollen of Maryland, the Budget Committee’s top Democrat, called Price’s bill “a political gimmick that does absolutely nothing to help create jobs.” He said Obama should be able to submit his budget how he chooses, without constraints from Congress.

The 253-167 vote fell mostly along party lines. The bill’s fate in the Democratic-controlled Senate is unclear.