The group’s oldest members — Senator Richard J. Durbin, 66, a progressive from Illinois who counts the Senate’s only socialist as a friend and ally, and Senator Saxby Chambliss, 67, a genial Georgia conservative whose nasty first campaign left lingering bad feelings among Democrats, and who is a confidant of Speaker John A. Boehner — illustrate that even with the mounting federal debt intensifying the partisan divide over spending and taxes, the severity of the fiscal threat is forging unlikely alliances.

If Mr. Durbin and Mr. Chambliss can cut a deal on Social Security and new tax revenues, their associates say, then just maybe all of Washington can come together.

For Republicans, that means accepting higher taxes and lower military spending. For Democrats, it would mean agreeing to curbs on the unsustainable growth of Medicare and Medicaid spending, as well as tweaks to Social Security, to avert a big shortfall in 2037 and as a trade-off for Republicans’ support on taxes…

The effort holds peril regardless of the outcome. If successful, a plan could be taken up as Congress debates this spring over raising the nation’s $14.2 trillion debt limit. But the group is hardly assured of support from Senate colleagues, let alone lawmakers in the House, where Republicans, including dozens of new Tea Party supporters, refuse to consider raising revenues. If the group fails, that would probably signal doom for the broader bipartisan effort Mr. Obama wants.