House Budget Committee Chairman Paul Ryan on Wednesday threw cold water on prospects for a grand bargain to tackle the looming U.S. fiscal crisis, saying the parties were too far apart on crucial issues. But he hopes a deal can be struck to restrain spending and overhaul the Social Security program, he said.

Mr. Ryan (R., Wis.) said he thought the coming debate over raising the country’s borrowing limit would lead to an agreement with Democrats for at least a “down payment” on tackling the federal government’s deficits and debt.

“Because we have such a difference of opinion on health care, it’s hard to imagine we’re going to have a global agreement,” Mr. Ryan said in an interview with The Wall Street Journal and Dow Jones Newswires in his Capitol Hill office. “Everyone wants to get a grand slam, but maybe we can get a single or a double.”

The interview occurred about two hours before President Barack Obama delivered a speech laying out his plan to address federal budget deficits.

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