(J. Scott Applewhite/AP)

“They appear to be at an impasse, provoked in this case by Democrats walking away from the Republican proposal,” Sen. John Thune (R-S.D.) said of the bipartisan panel. “And maybe that’s because they didn’t have a counter-offer ready to go. I hope they come back to the table, because I think the Republicans on the committee have demonstrated a willingness to go a long ways toward addressing and satisfying what some of the Democrat concerns are on revenues.”

Sen. Chuck Grassley (R-Ia.) echoed Thune’s comments, telling reporters that Democrats “walked away from the table, so it may be all over.”

“I don’t think the Democrats expected us to have a credible alternative,” Grassley said of the supercommittee talks. “They thought they could blame us. Well, we’ve offered a credible alternative. It isn’t like last summer, [House Speaker John] Boehner walking away from the table at the White House. The Democrats walked away from this table.”

but Sen. Patty Murray (D-Wash.), one of the co-chairs of the bipartisan panel, dismissed Republican claims that Democrats had walked away from the table.

“We haven't stepped away from anything,” Murray said, according to ABC News’ Sunlen Miller.

Senate Minority Whip Jon Kyl (R-Ariz.), one of three Senate Republicans on the 12-member panel, declined to say Wednesday when the supercommittee would hold its next meeting or whether the group would meet through the weekend.

Asked whether Republicans were now waiting for a Democratic counteroffer, Kyl replied, “Yes.”

As the battle behind the supercommittee’s closed doors has escalated, Democrats and Republicans have stepped up their rhetoric. Republicans have argued that their latest proposal is a major shift in their position on new tax revenue. It’s also a move that doubles as a defense against Democratic criticism that the GOP has been inflexible in its anti-tax stance.

“Oh, I think it’s a very reasonable one, and I’m disappointed that it was rejected out-of-hand by the Democrats,” Sen. John McCain (R-Ariz.) said of the GOP proposal. “It really is some revenue increases, which is quite a step forward on the part of Republicans.”

Democrats have questioned the substance of the proposal, calling it an “unserious” effort that does not include new tax revenue. But Senate Majority Whip Dick Durbin (D-Ill.) parted ways with many of his colleagues Wednesday morning when said it was a “breakthrough” that Republicans are even mentioning the word “revenue” in the negotiations.

“Well, I appreciate that; he must’ve looked at it,” Kyl said with a laugh when asked about Durbin’s comments.

Even so, Senate Republicans did not all promise to support the tax increases embedded in the GOP supercommittee offer.

“I’d have to look at it, I’d have to really look at it carefully,” said Sen. Orrin G. Hatch (R-Utah). “I don’t want to increase taxes. Revenues can be increased. And you can do it in a variety of ways without breaking any pledges and so forth.”

Asked if the proposal would raise revenues without breaking Republican pledges not to increase taxes, Hatch said: “I haven’t read what they’ve come up with. All I can say is it could be, if it’s done right.”

Sen. Mike Lee (R-Utah), a freshman who is a founding member of the Senate Tea Party caucus, also said he wanted to learn more about the proposal before committing to support or oppose it.

“I can’t weigh in on something when their work isn’t done and they don’t even have a complete proposal,” he said.

Thune argued that Republicans don not oppose finding more revenue but prefer “getting it the old-fashioned way, through economic growth.”

“There are some revenue proposals, I think, in what our side has put forward – although I’m not intimately familiar with the details of it – that don’t include tax revenue,” he said. “There are other forms of revenue that they raise. But I also think that they have been willing -- in order to get some rate reductions for business and individual taxpayers -- to give up some deductions and that sort of thing, broaden the base, so to speak.”

That kind of tax reform, Thune said, includes “things that probably most Republicans would probably find acceptable.”

Still, he said: “This is a moving process; it’s very fluid. I don’t think anybody is in a position right now to say, ‘I’m for this, or I’m for that.’”