The idea is to replace the across-the-board reductions that will hit programs effective and ineffective alike with more targeted cutbacks chosen by the White House.
"I don't think there's any real chance that the sequester is going to be undone" by Friday's deadline, Toomey said, "but we could pass legislation that would minimize disruption."
Toomey, working with other Republican senators, could introduce his plan as soon as Wednesday, and it could come up for a vote Thursday.
It is unlikely to pass the Democratic-controlled Senate - Obama bashed the idea Tuesday, and some Republicans don't like the plan - but the idea is competing to become a GOP talking point as both sides jockey over the $85 billion cuts expected to begin Friday.
Obama took aim at the idea that flexibility would salve the pain of 9 percent cuts to domestic programs and 13 percent to defense.
"When you're cutting $85 billion in seven months . . . there's no smart way," Obama said in Newport News, Va. "You don't want to have to choose between, 'Let's see, do I close funding for the disabled kid, or the poor kid? Do I close this Navy shipyard or some other one?' When you're doing things in a way that's not smart, you can't gloss over the pain and the impact it's going to have on the economy."
Democrats are wary of putting all of the responsibility for the cuts on Obama, fearing Republicans will attempt to absolve themselves of any blame for the fallout, even though in 2011 both sides agreed to the sequester as a penalty if they could not agree to a deficit-reduction plan.
Obama wants to replace the cuts with a mix of targeted reductions and new revenue generated by closing tax loopholes. Republicans oppose new taxes and want to shift the cuts away from defense programs.
Toomey said his plan would let the administration choose to preserve priorities - such as air traffic controllers - and apply deeper cuts elsewhere. Defense cuts would not be allowed to grow larger than currently scheduled.
Contrary to warnings from the White House, he said the cuts would help the economy.
"Given the disastrous fiscal situation that we're in, we've got to make these cuts," said Toomey, who is working with Oklahoma Republican Sens. Tom Coburn and James Inhofe.
The idea was backed Tuesday by Senate Minority Leader Mitch McConnell (R., Ky.) and, according to CNN, U.S. Rep. Paul Ryan (R., Wis.), the former GOP vice presidential nominee.
But Toomey's is one of several Senate Republican alternatives being discussed, and some in the GOP, including Sen. John McCain of Arizona, worry that it cedes too much power to Obama.
Contact Jonathan Tamari at firstname.lastname@example.org or follow on Twitter @JonathanTamari. Read his blog 'Capitol Inq' at www.philly.com/CapitolInq.