On the cusp of potentially pivotal budget talks Monday between the president and Congressional leaders, Members expressed some optimism Sunday that they could avoid a fiscal crisis but still clung to their partisan talking points and seemed determined to press their priorities.

“One of the reasons we are meeting tomorrow is that I think both the Democrats and the Republicans would like to come together and finish this negotiation and finish it sometime soon,” Senate Minority Leader Mitch McConnell (R-Ky.) said on ABC’s “This Week.” “It need not necessarily go to the eleventh hour.”

President Barack Obama has asked Congress to raise the federal debt ceiling no later than Aug. 2 to avoid default on the nation’s debts, but Republicans have balked and say the federal government first needs to get its spending under control.

To that end, the Senate will vote on a balanced budget amendment to the Constitution the week of July 18, McConnell said Sunday. House Majority Leader Eric Cantor (R-Va.) announced last week that his chamber would also take up such an amendment the week of July 25.

Passing the amendment “would be an important step in the right direction particularly looking out to the future,” McConnell said. “It would not eliminate the challenge that we have before us, which is to cut spending now, and that’s what these negotiations in connection with the request of the president, who has asked us to raise the debt ceiling, are about.”

McConnell is scheduled to meet with Obama and Vice President Joseph Biden at the White House on Monday evening to discuss reducing the deficit as part of a deal to raise the federal debt ceiling. Senate Majority Leader Harry Reid (D-Nev.) will meet separately with the president and vice president Monday morning.

McConnell reiterated his hard line against Democrats’ demands that revenues play a role in the final deal. “Throwing more tax revenue into the mix is simply not going to produce a desirable result, and it won’t pass,” he said.

A bipartisan group of lawmakers had been negotiating a deal with Biden until late last week, when Cantor and Senate Minority Whip Jon Kyl (R-Ariz.) left the table.

Revenue raisers, including ending tax breaks for such interests as oil companies, were the top sticking point. Republicans say they don’t favor any tax increases given the shaky economy.

Kyl indicated Sunday that he thinks Obama will ultimately agree to spending cuts without revenue raisers. “The key here is to get economic growth going again. We need to put people back to work,” the Arizona Republican said on “Fox News Sunday.” “If you want to kill the economy, raise taxes.”

Senate Republicans have “always been willing to consider so-called tax expenditures,” Kyl added, but in the context of overall tax reform that would result in a reduction of overall tax rates. “We’re not going to have time to do it” in the current debate, he said.

House Minority Leader Nancy Pelosi (D-Calif.) said that if there’s going to be a deal, House Democrats need to be at the table.

“There won’t be any agreement … unless the House Democrats are part of that, unless the Speaker comes to the table with 218 votes,” the former Speaker said on CNN’s “State of the Union.”

“I have no objection as former Speaker myself to the president and the Speaker trying to reach some level of agreement, some framework for how we go forward,” she later said. “That arrangement works if the Speaker has 218 votes. If they expect Democrats to vote for the agreement, then Democrats will have to be part of the agreement.”

One of her deputies, House Assistant Minority Leader James Clyburn (D-S.C.), also participated in the Biden discussions. He disagreed Sunday with Republicans’ contention that the Democrats’ proposed revenue raisers are tax increases.

“The fact of the matter is, we have on the table all kinds of revenue raisers that they keep calling tax increases. How do you call closing loopholes to oil companies that are making billions of dollars in profits, closing up these loopholes that would generate $40 [billion] to $50 billion in revenue, how do you call that a tax hike?” he asked on ABC’s “This Week.” “That is no tax hike.”

Two high-profile fiscal hawks, Sen. Jim DeMint (R-S.C.) and Rep. Michele Bachmann (R-Minn.), have both said they are unwilling to vote to raise the debt ceiling, even if it means difficult financial straits for the country. But both discounted on Sunday talk shows the idea that the government would actually default.

“Well, I do care if [the government] defaults, but the fact is, Candy, we won’t,” DeMint said on CNN’s “State of the Union.” “If we never raise the debt ceiling again, we’re going to pay our bills, we’re going to pay Social Security.” He added that if Congress raises the debt ceiling without taking control of spending, “I think you’re going to see the markets respond in a much worse way as people look in and realize we don’t have the will to stop this spending.”

Bachmann, who will formally announce her 2012 presidential campaign Monday, pushed back against the predictions of default as debt scare tactics. “I have no intention of voting to raise the debt ceiling,” she said on CBS’ “Face the Nation.” “I’ve seen smoke and mirrors time and time again. … That cycle has to stop.”

McConnell, however, said the debt ceiling talks are “a great opportunity to bring the two sides together to do something really significant for the country. … I think what would reassure the world more than anything we could do would be to come together and use this opportunity, presented by the president’s request of us to raise the debt ceiling, to do something about the debt.”

He added that “the president’s own trustees, of Medicare and Social Security, have said both programs are in trouble” and that Medicare expenditures might be a point of potential compromise. “We know the Democrats are willing to reduce Medicare expenditures,” he said on “This Week.” “That’s something that can actually pass the Congress.”

Melanie Starkey contributed to this report.