"The reality is, you're going to have to have a deal here," Cole said, appearing on Bloomberg Television's "Political Capital with Al Hunt" airing Friday night. "And a deal means everybody gives something up."
In an interview Thursday with Nevada public radio station KNPR, Reid, the Senate majority leader, agreed that a large-scale grand bargain wasn't in the cards.
"They have their mind set on doing nothing, nothing more on revenue, and until they get off that kick, there's not going to be a grand bargain," Reid said. "We're just going to have to do something to work our way through sequestration."
Ryan, his party's vice presidential nominee a year ago, and Senate Budget Committee Chairwoman Patty Murray, D-Wash., are two of the key congressional figures in the talks. Both say they're seeking common ground between the sharply different Republican and Democratic budgets.
Common ground, however, is a much different concept than compromise. It involves finding ideas upon which they can agree rather than compromising principles such as Republican opposition to tax increases or the unwillingness by many Democrats to consider cutting future Social Security benefits by decreasing the annual cost-of-living adjustments.
Instead of a broad agreement encompassing tax hikes and structural curbs on the growth of benefit programs like Medicare and Medicaid, Ryan says he's seeking a "smaller, more achievable objective."
The talks, he said, also will focus on alleviating another upcoming round of automatic spending cuts and replacing them with longer-term cuts.
Sequestration mostly hits so-called discretionary spending, the money approved by Congress each year to run agency operations. Ryan wants to cut autopilot-like spending on entitlement programs like Medicare to ease sequestration's effects on both the Pentagon and domestic programs.
"I think we all agree that there's a smarter way to cut spending" than sequestration, Ryan said. "If I can reform entitlement programs where the savings compound annually ... that is more valuable for reducing the debt than a one-time spending cut in discretionary spending."