But the Republicans did not sound like they were in a mood to budge.
The administration of President Barack Obama also denied suggestions it is hyping the consequences of the so-called sequester -- $85 billion in military and domestic spending cuts crammed into the seven remaining months of the fiscal year.
Gene Sperling, a top economic adviser to Obama, made the rounds of morning talk shows to press the case that the president is still working the phones and seeking out lawmakers in both parties who are open to an alternative way to trim the bloated $1 trillion a year deficit.
Sperling said a Republican proposal to give the president more leeway in deciding what funding gets cut is not enough. The spending bludgeon will cost 750,000 jobs in an economy that is fragile, he said.
"When you have those type of harsh spending cuts in such a short concentrated period of time, it's like saying to somebody you can cut off three of your fingers, but you can have the flexibility to choose which ones you want to cut off," Sperling said on ABC News.
"My belief is that as this pain starts to gradually spread... more Republican colleagues who are concerned about this harm to their constituents will choose bipartisan compromise."
Obama signed an order bringing what he called the "dumb" spending cuts into effect Friday after a last-ditch meeting with congressional leaders went nowhere.
The measures could mean long lines at US border posts, reduced military readiness, cuts to special needs education programs, and will trim the resources of some emergency services, according to White House officials.
The cuts were never meant to take effect but rather were a poisoned pill clause attached to a 2011 agreement to raise the debt ceiling, and designed to be so scary that lawmakers would find a less drastic way to cut the deficit.
They failed and the sequester is here, although its effects are expected to take weeks to be felt.
"When this sequester goes off, yes, it's not going to hurt as much on day one," Sperling said.
"But, again, every independent economist agrees it is going to cost our economy 750,000 jobs, just as our economy has a chance to take off."
Obama is pressing for what he calls a more balanced approach that includes concessions: changes to entitlement programs, like medical care for the elderly and poor, as sought by Republicans.
But he wants any deal to include fresh revenue from closing tax loopholes enjoyed by companies and wealthy Americans.
Obama won a showdown late last year over the fiscal cliff -- which threatened to let across-the-board George W. Bush-era tax cuts expire -- when Republicans agreed to higher taxes on the rich.
But they drew the line there, and now insist that any deficit deal has to focus solely on cutting spending.
"He got his tax hikes. It's time to cut spending. And every American knows it," House of Representatives Speaker John Boehner told ABC.
Boehner said neither Republicans nor Democrats were likely to cry uncle any time soon and eliminate the sequester.
"I don't think anyone quite understands how it gets resolved," Boehner said.