Washington (CNN) -- As the clock ticks down to the August date in which the U.S. officially defaults on its debt, lawmakers on both sides of aisle appear to be playing a game of political volleyball.

It was evident during President Obama's news conference Wednesday in which he chided congressional Republicans for the impasse on the debt ceiling talks.

"They are in one week, they are out one week," he said. "You need to be here. I've been here. I've been doing Afghanistan and bin Laden and the Greek crisis."

Read more of Obama's remarks

On Thursday, Senate Minority Leader Mitch McConnell called Obama's bluff, inviting him to Capitol Hill for talks. The news came after Senate Majority Leader Harry Reid announced that the July 4 recess would be canceled.

House members, meanwhile, are on one of their weeks at home, instituted when the GOP took over in November. The goal is to provide greater access for constituents. They'll be back in Washington on July 6.

"I'd like to invite the president to come to the capital today to meet with Senate Republicans ... (on) why what he's proposing will not pass, " McConnell said. "And we can discuss what he has in mind. And we can start talking about what's actually possible."

"We're waiting," McConnell added.

The president had a much publicized fundraising trip to Pennsylvania on Thursday. In his daily press conference, White House press secretary Jay Carney said Obama would not cancel the events -- and that leaders from both parties had already met with the president at the White House this week.

Other Senate Republicans are furious that Obama isn't willing to change his plans.

"Where is the president? Campaigning," said Sen. Rand Paul, R-Kentucky. "We are here Mr. President and we will have an offer. We don't want to raise the debt ceiling."

"As Republicans, for the good of the country, we are willing to raise the debt but only, and I repeat only, if we have significant budgetary reform," he added.

On the other hand, Sen. Pat Roberts, R-Kansas, said that while the Senate will be in session, "we're going to be here unfortunately not working on a deal because a deal doesn't exist."

"Now he says it isn't worth his time to come down and talk to Republicans," he said. "I remember when he talked to Republicans before and all we got was a lecture. So maybe if he'd just take a valium and calm down and come on down and talk to us, it might be helpful."For his his part, Reid said negotiations must continue. Failure to raise the debt ceiling, he warned, would plunge the economy into a "full-fledged depression."

"The work we're doing to cut the deficits and create jobs is too important, the obstacles too steep and the time too short to waste even a moment," the Nevada Democrat said. "There's still so much to do to put American back to work and cut our deficits."Is the debt ceiling unconstitutional?

Senate Democrats are irate over what they say is the GOP's willingness to walk away from the talks.

"They've taken this extraordinary step of walking away, walking away from their responsibilities, walking away from the American people, walking away from a meeting of the Senate at this extraordinary moment," said Sen. John Kerry, D-Massachusetts, on Thursday after several Republicans failed to attend a Senate Finance Committee meeting on free trade legislation.

Sen. Chuck Schumer, D-New York, accused Republicans of wanting the country "to be in as bad shape as possible because that might help them electorally."

The whole impasse stems from the fact that GOP leaders have shown no signs of yielding in their opposition to higher taxes as part of any grand bargain with the White House. Recent bipartisan talks led by Vice President Joe Biden collapsed over the tax disagreement.

It was a point that Obama repeated at his press conference, saying that both parties need to be willing to "take on their sacred cows and do tough things" while moving away from "maximalist positions."

Boehner said Obama is "sorely mistaken if he believes a bill to raise the debt ceiling and raise taxes would pass the (Republican-controlled) House."

Top economic analysts have warned of potentially catastrophic repercussions if the ceiling is not raised by August 2, including skyrocketing interest rates and a plummeting U.S. dollar.

CNN Chief Political Analyst Gloria Borger said that when a president goes out of his way and really attacks the other party "it gives you a sense of how the deal inside the room could really be in the process of collapsing."

Read Gloria Borger's column

"I mean this doesn't help House Speaker John Boehner get back to that negotiating table, really does not."

David Gergen, CNN's senior political analyst and former aide to several presidents, agreed.

Read David Gergen's column

"One had a very distinct sense today that they are not making the kind of progress the country needs in these talks or he would not have taken the tone he did today," he said. "If you're in a critical moment when you're trying to build trust, you don't go public and scold the other side and issue all these sort of snide insults about them."

CNNMoney.com's Jennifer Liberto contributed to this report.