Washington (CNN) -- As Congress leaves town for its August recess, President Barack Obama and congressional Republicans are trying to lay the groundwork for who will have the most leverage when they return to take up the issues of funding the federal government and raising the nation's borrowing limit.
Both sides say the stakes are high -- that may be the only thing they agree on.
"We've seen a certain faction of Republicans in Congress hurt a fragile recovery by saying that they wouldn't pay the very bills that Congress racked up in the first place, threatening to shut down the people's government if they can't get rid of Obamacare," the president said Tuesday during an event pushing his jobs proposals in Chattanooga.
But some Republicans say it's Obama who's threatening to shut down the government.
"Instead of working together, the president yesterday threatened to shut down the government and recycle some of his old partisan proposals," House Speaker John Boehner countered on Wednesday.
Factions of Republicans in the House and Senate vow not to fund the government when it runs out of money on September 30 if funds are provided for the president's health care reform program, saying this is their last and best chance to try to derail it.
"The pushback we get from that from some people is, 'Well, that's crazy, because that means you're willing to shut down the government over Obamacare.' That's not the way I see it. The way I see it is, if we pass a budget that pays for everything except Obamacare, and the president says he'll veto that, it is he who wants to shut down the government," Sen. Marco Rubio, R-Florida, said Tuesday.
But other GOP lawmakers, such as Sen. Richard Burr of North Carolina, have criticized that threat.
"I think it's the dumbest idea I've ever heard of," Burr told The Associated Press.
Some in the GOP are also threatening to possibly use the nation's debt ceiling to wrestle some concessions from the White House -- something administration officials have adamantly rejected.
"I am not negotiating around the debt ceiling," Obama told House Democrats in a meeting Wednesday, according to a senior Democratic aide.
As Congress gets ready to go home at the end of this week -- and a possibly another August full of heated town hall meetings on everything from the budget to Obamacare to immigration -- both the White House and congressional leaders are jockeying for maximum political advantage.
A majority of Americans don't approve of how the president is handling the economy and their unfavorable opinion of Congress continues to grow.
The president is also trying to up the pressure on Congress on another front -- the automatic spending cuts that neither side initially said they wanted.
Despite dire warnings of economic peril if the cuts went into effect, Congress couldn't agree how to cancel the first round last spring. Further reductions are scheduled for next year.
The cuts were discussed in meetings the president had Wednesday with Democrats on Capitol Hill.
"Sequestration was a big topic in there," Sen. Joe Manchin, D-West Virginia, told reporters.
The government reported Wednesday the gross domestic product -- the broadest measure of economic activity -- rose at a 1.7% annual rate in April through June, slightly faster than the 1.1% rate in the first quarter.
So far cuts in government spending have only subtracted less than a tenth of a percentage point from GDP growth, but economists are expecting the impact from government cuts to wane in the months ahead.
Obama, in his speech on Tuesday, talked about how specific businesses, such as those contracting with the military, are especially being hurt. He also cited a Congressional Budget Office report estimating those across the board cuts will cost 750,000 jobs this year and 900,000 next year.
"Instead of reducing our deficits with a scalpel to get rid of programs we don't need, but keep vital investments that we do, this same group has kept in place this meat cleaver called the sequester that is just slashing all kinds of important investments in education and research and our military," he said in Chattanooga.
The budget office also had a warning sign saying canceling the cuts and thereby increasing the debt "... would diminish policymakers' ability to use tax and spending policies to respond to unexpected future challenges and would increase the risk of a fiscal crisis" possibly by losing the ability to borrow money at affordable rates.
Republicans have argued those automatic cuts were the only way to force real reduction in government spending.
House Budget Chairman Rep. Paul Ryan said earlier this year he didn't think taking 2% off the top in a $14 trillion economy would be a big drag on growth.
Senate Minority Leader Mitch McConnell however previewed his bargaining response to the president.
"You want sequester relief? Then let's talk about a reduction in entitlement spending," he told National Review. "It's a question of what kind of spending reduction is best for the country, and that's a framework that could make sense."
CNN's Deidre Walsh and Greg Seaby and CNN Money's Annalyn Kurtz contributed to this report.