House Republicans say they can get rid of the federal deficit in just 10 years without raising taxes.
House Budget Committee Chairman Paul Ryan, R-Wis., said the new plan does keep government spending growing but at a slower rate.
Ryan said the GOP plan will help the economy grow and thus bring more tax revenue into Washington.
The measure would also try to repeal Obamacare and cut spending in other places.
"We owe the American people a balanced budget," Ryan told "Fox News Sunday" host Chris Wallace.
The former GOP vice presidential candidate said repealing the plan, which he says is harmful to American's health, would help save money.
"We believe that Obamacare is a program that will not work," Ryan said. "We believe Obamacare will actually lead to hospitals and doctors and health care providers turning people away."
"It's a program that basically puts Medicare under the control of 15 people on a board that will determine what kind of benefits people get. That's a rationing board however you slice it. We don't think health care is going to be improved in this country," he said.
Not every Republican believes it's possible to repeal Obamacare, but Ryan said getting rid of it will strengthen Medicare's finances.
"We say we get rid of Obamacare, we end the raid, and we apply those savings to Medicare to make Medicare more solvent and extend the solvency of the Medicare trust fund," Ryan said.
When Wallace called the repeal a non-starter, Ryan replied, "Well, we believe it should. That's the point."
The White House is not likely to go along with the plan, but it hasn't introduced a budget of its own. The administration's budget was supposed to be released on Feb. 4. It may not be out till next month.