Senate Republican leader Mitch McConnell of Kentucky made a strong statement of support for the measure.

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"Not only is this legislation just the kind of thing Washington needs right now, it may be the only option we have if you want to see the debt limit raised at all," he said.

"I strongly urge my Democratic friends to join us in supporting it."

Despite his warning, McConnell and Reid have been deeply involved in writing a fallback measure that is viewed in both houses as promising.

It would allow the president to raise the debt limit by $2.5 trillion in three installments over the next year without a prior vote by lawmakers. Instead, a panel of House and Senate members would be created to recommend cuts in benefit programs, with their work guaranteed a yes-or-no vote in the House or Senate.

Recreating the divide that plagued the earlier negotiations, Democrats want the panel to have the power to recommend higher taxes.

Neither Reid nor McConnell has publicly disclosed the details of the measure, and neither is expected to do so as long as the legislation in the House is pending.

One conservative deficit hawk, Sen. Tom Coburn, unveiled his own proposal to bring federal deficits under control. The Oklahoma Republican recommended $9 trillion in cuts over a decade, including $1 trillion in higher taxes.