Protests continue as states consider drastic cuts to trim budget deficits.
Congress has four days to stop a shutdown of the federal government with a short term spending bill.
President Obama has agreed to $4 billion in spending cuts as part of a compromise with Republicans.
"Everybody should be prepared to give up something in order to solve our budget challenges," he told a meeting of governors Monday.
The budget crisis is symbolized by the showdown in Wisconsin, where protesters are still camping out at the state capitol.
Wisconsin public employees' unions now say they're willing to negotiate pay cuts, but Republican Governor Scott Walker is refusing, saying he wants to force unions to take cuts and to give up their bargaining rights to cut costs and, he says, "to make history".
"I know that collective bargaining has a cost and when I'm cutting more than $1 billion from aid to local governments, in this next two-year budget, I need to do what no other governor is doing across the country," Walker said on "Meet the Press" Sunday.
The president opposes Walker's move.
"I don't think it does anybody any good when public employees are denigrated or vilified or their rights are infringed upon," Mr. Obama said.
He also offered a compromise on another hot budget issue, telling states to design their own health care plans if they think they can cover the same people at the same cost.
"You can implement that plan and we'll work with you to do it," the president said.