WASHINGTON -- A group of Senate Republicans, including Georgia's Johnny Isakson and Saxby Chambliss, offered a way out of Congress' unemployment insurance pickle Wednesday. And they threw in a fix for military pensions and a get-tough measure on undocumented immigrants, for good measure.

New Hampshire Sen. Kelly Ayotte's proposal would pay for a $6.4 billion long-term unemployment insurance extension and restore $6 billion in cost of living increases for early military pensions – dinged by the December budget agreement – by preventing undocumented immigrants from claiming a tax credit for their children.

“We can fix it in the right way,” Chambliss said of the military pension issue. “Senator Ayotte has come up with a great pay-for that is an All-American pay-for. It is one that needs to be enacted in the short term in this bill.”

A three-month extension of unemployment benefits barely cleared a procedural hurdle Tuesday morning but will advance no further without an offset for the price – as multiple Republicans who backed it made clear. Another 60-vote hurdle is needed to end debate. Chambliss and Isakson voted against the benefits but have said they would consider backing the bill if it's paid for.

An inquiry to Senate Majority Leader Harry Reid’s office on the bill was not returned. In a floor speech this morning Reid said he would be open to finding ways to offset the cost of the benefits, but not offsets that attack Obamacare or the nation’s children.

“There’s only one reason that the Majority Leader wouldn’t let this amendment go to the floor, and that is if he wants a problem rather than a solution,” Isakson said, referring to the browbeating Democrats are giving Republicans on unemployment insurance.

“I hope the Majority Leader would let this come to the floor and solve three problems with one amendment.”