White House: No negotiations 'when there is a gun pointed to your head'

"What we're not going to do is entertain those kind of solutions when there is a gun pointed to your head," Palmieri told MSNBC.

That seemed to rule out the administration agreeing to any changes to ObamaCare as part of a deal on the federal budget or debt ceiling.

Earlier Tuesday, Sen. Dick Durbin (D-Ill.) said it was "conceivable" that reforming some aspect of ObamaCare would be included in a final deal.

"We can work out something, I believe, on the medical device tax. That was one of the proposals from the Republicans," Durbin told CNN. "As long as we replace the revenue so that we don’t put a hole in our deficit and respond to this in a responsible fashion. That’s one thing the Republicans want to talk about it. Let’s sit down, and put that on the table.”

But Palmieri said it was "apparent" that there was bipartisan agreement around a so-called "clean" continuing resolution that would keep the government funded for the next six weeks, allowing lawmakers time to negotiate larger compromises for a budget deal that would cover the remainder of the year.

She added that there was not "a lot of substance to talk about" in regard to the temporary measure that would extend for the next six months.

"This is not the type of thing you do some big negotiation about," she said.