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Rep. Paul Ryan, Wisconsin Republican and chairman of the House Budget Committee, compared the U.S. debt situation with being “the healthiest-looking horse in the glue factory.”

“So we do not have a debt crisis right now, but we see it coming. We know it’s irrefutably happening, and the point we’re trying to make with our budget is, let’s get ahead of this problem,” said Mr. Ryan on “Face the Nation.” “If we keep kicking the can down the road, if we follow the president’s lead or if we pass the Senate budget, then we will have a debt crisis.”

House Republicans released last week a budget, helmed by Mr. Ryan, that would cut $4.6 trillion over 10 years, all through spending reductions, while Senate Democrats are working on a plan that includes $1.8 trillion in deficit reduction through a combination of tax increases and spending cuts.

Both sides agreed there was reason for optimism about reaching a compromise. “At least the Senate’s doing something now,” said Mr. Ryan, a reference to the Senate’s inability to pass a budget for the past four years.

“Hopefully we can go to conference on these budgets, and hope springs eternal in my mind,” said Mr. Boehner.

Ms. Klobuchar called it an “exciting time” and “a great time of opportunity” to reach agreement on a budget deal.

“I think there’s a real urgency in Washington, particularly in the Senate, that I’ve never seen before,” she said.