With August poll ratings for the president and Congress in a tailspin after the messy debt deal and a report of stagnant job creation, GOP leaders are breaking out their olive branches.

Indeed, the rhetoric of the top two House leaders, Speaker John Boehner (Ohio) and Majority Leader Eric Cantor (Va.), has softened since the August recess, when many of their Members were confronted at home by constituents fed up with Washington, D.C., and concerned primarily with unemployment.

For example, the GOP leadership’s early reaction to President Barack Obama’s jobs speech outlining a new $447 billion package was skeptical, but far from the usual harsh broadsides many have come to expect.

Cantor appeared to go out of his way to look for common ground with the president after his address to Congress on enacting free trade agreements, on reforming unemployment insurance and even on accelerating infrastructure investments. The leadership team also sent a conciliatory letter to the White House Friday asking the president to submit his bill and promising it would receive consideration from House committees.

“There’s definitely a change in the rhetoric — it remains to be seen whether there’s going to be a change in policy,” said Rep. Steven LaTourette (R-Ohio). He attributed the change to Members listening to voters in August.

“A lot of base Republican supporters in my part of the world said, ‘You know, you have to show us something. … This cut-and-grow thing has a limited shelf life. You actually have to produce something, and if you can work with the president, you should, to get something done because everybody wins,’” LaTourette said. “I think they probably heard the same thing and I think that’s great.”

But the Ohio Republican, who is a close ally of Boehner, said that he’s not sure it will actually lead to a broad deal on a jobs bill or much else.

“We continue to have a group of people in both parties that you can never make happy, and we’ll see how that plays out,” he said.

Rep. Tom Cole also acknowledged the leadership’s less combative stance.

“Our leaders have said, ‘Keep your powder dry. Let’s give him a chance to make his case,’” the Oklahoma Republican said.

Cole said that nobody is happy with how the debt limit crisis ended, and voters are unhappy for various reasons. In his district, Cole said, many Republicans didn’t understand why he compromised at all on the debt ceiling.

But at a larger level, voters “want us to work together,” he said.

To that end, leaders are working hard to avoid the kinds of showdowns that have brought the government to the brink of financial calamity twice in the past year.

Cole, a former chairman of the party’s campaign committee, said that with next year being an “anti-incumbent year and an anti-Washington year,” it behooves Republicans to keep the focus on Obama.

“I do think we want to avoid making ourselves the issue,” Cole said, praising Boehner for averting both a potentially catastrophic default on the nation’s debt and a government shutdown earlier this year.

“Boehner hasn’t gotten the credit he deserves for saving us from ourselves,” Cole said.

The new tone at the top wasn’t shared across the GOP, with Republicans fractured over Obama’s proposal to extend and expand the payroll tax cut for workers and extend it to businesses as well. While Cantor expressed an openness to extending the payroll tax cut this week, Rep. Pete Sessions (R-Texas), the party’s campaign chief, respectfully disagreed.

“It is a horrible idea, we should not do it,” Sessions said, saying it undermines Social Security.

Sessions contended that allowing the payroll tax cut to expire wouldn’t be a tax increase, but “correcting” the “mistake” of cutting the tax in the first place.

Other Republicans in both chambers split on the payroll tax cut, which is the centerpiece of the president’s proposal. And the party’s more conservative Members continued to launch broadsides against the president — some even filmed speech responses and sent them to reporters before the president took the podium.

But the shift from the leadership has not gone unnoticed among Democrats.

Rep. Raúl Grijalva (D-Ariz.), co-chairman of the Progressive Caucus, said the GOP is starting to wake up to voters’ focus on jobs.

“I think they are reading the same polls that Democrats are reading. … And quite frankly, they went home for a month and they heard it,” he said. “All of us heard the same thing when we went back home: get something done, quit playing games, and quit holding your breath.”

Rep. Peter Welch (D-Vt.) said “being within an eyelash of default” during the debt limit debate spooked a lot of Members who are now looking to find common ground on the issue of jobs.

“We crossed a river during the debt limit crisis that I think some people don’t want to go back to,” the Vermont Democrat said. “I think a lot of people are feeling pretty discouraged from that experience.”

Welch has formed a bipartisan alliance to deal with recovery efforts relating to Hurricane Irene, which ravaged the eastern seaboard from Vermont to Cantor’s Virginia district and beyond. Cantor’s district also was the epicenter of a 5.8 magnitude earthquake that rattled the East Coast in August. The two lawmakers with disparate political views have publicly complimented each other on working out a compromise to help citizens displaced by the natural disasters.

Whether that kind of bipartisanship will last through the fall is an open question, Welch said, but Members have an incentive to give it a try.

“A lot of our constituents have just given up on the institution,” Welch said. “They don’t see Congress as being capable of fixing any problems, and the only thing we can do is work together to find some common sense solutions.”

Jessica Brady contributed to this story.