Updated: 11:31 a.m.

Speaker John Boehner on Sunday dangled the possibility of a comprehensive agreement to raise the debt ceiling and pare down the debt and deficit over 10 years, saying his final offer to President Barack Obama that included $800 billion in revenues through tax reform was still on the table.

However, the Ohio Republican was pessimistic about the prospects of reviving such a deal in time to meet the Aug. 2 deadline to avoid a U.S. default and said his focus was on negotiating a new plan with the bipartisan Congressional leadership that is based on the parameters of the Cut, Cap and Balance proposal that passed the House last week before promptly failing to garner even one Democratic vote in the Senate.

“It may be pretty hard to put Humpty Dumpty back together again. But I’ve never taken my last offer off the table,” Boehner told “Fox News Sunday” host Chris Wallace. “I’m going to continue to work with my colleagues in both parties to develop a framework within [the Cut, Cap and Balance plan]. It could come together, but it’s not available yet.”

Boehner accused the president on Friday of “moving the goal post” in a potential agreement over a package that included $800 billion in revenues, and the Speaker suddenly walked out on the negotiations in a reprise of his Saturday evening pullout from talks two weeks ago. He said the president had “demanded $400 billion more” in the form of raising taxes on businesses that create jobs, a characterization that the White House disputed.

Boehner said Sunday that bipartisan negotiations among Congressional leaders in both the House and Senate were ongoing, adding that he hoped enough progress could be made to stanch market unrest in Asia and the United States. The Asian markets open Sunday afternoon local time. But the Speaker said his first concern was not overseas market reaction, but developing a plan that was in the best interest of the United States.

Boehner said he hoped to have a new debt ceiling proposal ready later Sunday and said Republicans were prepared to move ahead without Democratic support if talks aimed at developing a bipartisan solution fail. Following a meeting at the White House on Saturday with Obama and other Congressional leaders, Boehner met separately in his Capitol office with House Minority Leader Nancy Pelosi (D-Calif.), Senate Majority Leader Harry Reid (D-Nev.) and Senate Minority Leader Mitch McConnell (R-Ky.).

“I would prefer to have a bipartisan approach to solve this problem,” Boehner said. “If that’s not possible, my Republican colleagues and I are prepared to move on our own.”