Murray also said that tax reform was a priority for her.
"I would agree with the Chairman that we do need to do tax reform," she said on NBC. "Where the divide comes is what you would do with any of the revenue that was generated from that. But that doesnt mean we couldn't ever find a compromise with that."
The two budget chairs said that while the budget deal doesn't guarantee a grand bargain any time soon, the agreement has paved the way for more compormise in divided government.
"This isn't a large agreement, but this is a symbolically large agreement," Ryan said. "You gotta crawl before you can walk before you can run."
Murray agreed that the budget deal was a victory for compromise.
"We can't take on the tough discussions until we learn to use the word 'compromise,' so that we can have that be a respected, trusted word in this Congress," she said. "We're trying to bring some respect to the word 'compromise.'"