Sen. Pat Toomey and more than 30 Senate colleagues will introduce the "Ensuring the Full Faith and Credit of the United States and Protecting America's Soldiers and Seniors Act."
The bill is meant to offer a stop-gap if Congress refuses to raise the debt ceiling and the Treasury Department thus falls short of having enough cash to pay all the government's bills in full and on time.
Toomey's proposal would require that revenue going to Treasury first be used to pay interest on U.S. debt, Social Security benefits and active-duty military pay.
If there's not enough revenue available to cover those payments when they're due, the bill would also give limited authority to Treasury to raise the debt ceiling just enough to borrow the difference between revenue on hand and what's owed on the priority payments.
The bill would actually be a 2.0 version of legislation the same group introduced in July 2011 during the country's last debt ceiling imbroglio. The only major difference is that this year's bill would let Treasury raise the debt ceiling to make prioritized payments.
Chances are good, however, that the White House and Treasury will not be any more receptive to the new version than they were to the original.
"Choosing whether you pay Social Security beneficiaries, or combat troops in Afghanistan, or veterans who depend on the VA for benefits, or bond holders -- these are choices about default," White House press secretary Jay Carney said on Thursday.
Treasury didn't offer a response, but referred CNNMoney to comments Treasury Secretary Tim Geithner made in 2011 in response to a proposal to prioritize interest payments on U.S. debt.
"This 'prioritization' proposal advocates a radical and deeply irresponsible departure from the commitment of Presidents of both parties throughout American history, to honor all commitments our nation has made," Geithner wrote in a letter to a senator.
Practically speaking, Treasury collects enough revenue in a month to pay interest, Social Security and active military, which combined represent about a quarter of what's owed.
But bills come due every day and the revenue available to Treasury differs, sometimes radically, from day to day.
For instance, the Bipartisan Policy Center estimates that $30 billion of interest will be due on Feb. 15, but only $9 billion in revenue would be available to pay the $52 billion in legal obligations due that day.
What's more, Treasury's systems -- which process more than 80 million payments a month -- are set up to pay bills as they come due without regard to the type of payment. Interest payments, however, are processed separately.
By most accounts the payment system is a complicated one. So it's not clear how long it would take to make changes to allow Treasury to prioritize.
And there's concern that any temporary band-aid to a debt ceiling impasse would not do much to protect the U.S. economy let alone its reputation with creditors.
The Center estimates that, absent an increase in the debt ceiling, Treasury would only be able to pay about 60% of what's owed, meaning reams of delayed payments. That could take a big bite out of economic growth. And being late on so many payments would likely "prompt a downgrade even as debt obligations continued to be met," credit rating agency Fitch said this week.