Rep. Paul Ryan (R-Wis.) talks with Iowa Gov. Terry Branstad, left, after presenting him with a cheesehead hat during Branstad's birthday bash and fundraiser Saturday in Altoona, Iowa. (Charlie Neibergall/AP)

Gov. Terry Branstad (R) brought one of his party’s shining stars to this presidential crucible last Saturday night before nearly 800 important Iowa Republicans, stoking speculation that the guest, Rep. Paul Ryan (Wis.), was testing the 2016 waters.

But moments after Ryan’s speech, Branstad nixed any thought that the 2012 vice-presidential nominee should be his party’s next standard-bearer. “Leadership is going to come out of the states, not Washington. Look at the governors,” Branstad said in an interview.

That refrain has been echoed repeatedly around the nation in the past week, with many GOP leaders now viewing the congressional Republican brand as so toxic that only chief executives in state capitals should be contenders in 2016.

Wisconsin Gov. Scott Walker said on ABC’s “This Week” that neither his friend Ryan nor other rising Republican stars in Congress should run for president, saying “it’s got to be an outsider” as the nominee. Another of Ryan’s closest friends, House Majority Whip Kevin McCarthy (Calif.), ruled out any member of Congress. “I don’t think anyone should become president if they haven’t been a governor first,” he told MSNBC’s “Daily Rundown” last week.

This growing chorus from party elders comes as the Republican Governors Association convenes this week in Arizona, providing a showcase of GOP talent not associated with Congress.

It’s also the culmination of a roller-coaster ride in Washington. Both major parties have been whipsawed by strategic policy mistakes that have battered their images. First the public lashed out at Republicans for forcing the 16-day government shutdown last month, driven by the GOP’s single-minded focus on trying to repeal President Obama’s health-care law.

Then voters recoiled from Obama and Democrats as they found a health-care Web site that wouldn’t work and several million of them received notices informing them that their current insurance plans would be terminated.

Obama’s approval ratings plunged precipitously, while Congress hit another record low.

To Republicans, the Obama decline is akin to what President George W. Bush suffered in late 2005, when the Iraq war and the GOP administration’s handling of Hurricane Katrina combined to create the broad sense that his administration had lost its ability to govern. This created a huge opening for Democrats in 2008, when Obama used his new stature in Washington to run as an outsider who would change the way business was done in the capital.

Congressional Republicans have several relatively youthful lawmakers who are considering 2016 bids and who might try to follow Obama’s outsider path, but with conservative characteristics: Ryan, 43, and Sens. Ted Cruz (Tex.), 42; Marco Rubio (Fla.), 42; and Rand Paul (Ky.), 50. Cruz, Rubio and Paul are all in their first Senate term, just as Obama was when he announced his presidential bid in early 2007.

But party elders increasingly view this crop as badly tainted by the nearly three-year run of congressional crises in showdown after showdown with Obama. Instead, they’re looking at governors who can win elections in states that also supported Obama, and then have demonstrated how to govern effectively in those blue-leaning states.

“These governors are examples to our party of successful governors in Democrat states and being able to succeed in getting Democrat and independent votes. I think it should be an example to all of us,” Sen. John McCain (Ariz.), the GOP’s 2008 presidential nominee, told reporters.

He named Republican Govs. Chris Christie of New Jersey, Bobby Jindal of Louisiana, John Kasich of Ohio and Susana Martinez of New Mexico as potential contenders he would support.

McCain summed up his view in one number: “Look at the approval rating of Congress: 9 percent.”

Part of this is history. Republicans have not elected a president directly from Congress since Sen. Warren G. Harding (Ohio) in 1920. Most of this view, however, has been prompted by a strong crop of governors who have established profiles that are separate and distinct from Republicans on Capitol Hill.

Christie won reelection this month by a large margin, claiming a majority of Hispanic voters and a larger-than-normal percentage of black voters for a Republican. The next day, Sen. Orrin G. Hatch (Utah) practically endorsed him for 2016 and suggested that Martinez serve as his running mate.

Sen. John Cornyn (Tex.), who ran the GOP’s Senate campaign operation for four years, declined to suggest the biography he was searching for but noted that the anti-Congress view makes some sense. “I think I understand where they’re coming from, looking at the congressional approval rating,” Cornyn, who is now the No. 2 GOP leader in the Senate, said this week.

A large share of the public’s disdain for Congress has landed on the lap of House Speaker John A. Boehner’s Republican conference, and Cruz, who helped steer the strategy in both chambers that led to the shutdown.

By the time the shutdown ended in mid-October, disapproval of the way Republicans in Congress handled budget negotiations jumped to 77 percent of voters, up from 63 percent just three weeks earlier, according to a Washington Post-ABC News poll.

Some congressional GOP contenders have grown agitated by the conventional wisdom about governors. Ryan was particularly displeased when asked whether the 2016 nominee had to be a governor.

“No,” Ryan said Tuesday at a Washington meeting of corporate chief executives convened by the Wall Street Journal. “Next question.”

After a pause and some laughs from the crowd, he added: “The résumé is not as important to me as the person, as the quality of their ideas, as their track record of reform.”

Back in Iowa, however, Branstad disagreed. One of Ryan’s biggest supporters, the Iowa governor brought the House Budget Committee chairman to the state knowing it would serve as his first big foray into the state that serves as the initial presidential testing ground.

After Ryan spoke, Branstad praised his fiscal proposals to rein in entitlement spending and said he grew fond of the fellow Midwesterner as they campaigned together last fall when GOP nominee Mitt Romney selected Ryan as his running mate.

Despite that experience, Branstad was adamant that he doesn’t want Ryan to run for president and instead wants him to keep up the fight in Congress.

“I really think he’s a sincere man. . . . He’s one of the few people in Washington that gets it and understands what needs to be done, and I’d like to see him play an important leadership role in getting our nation’s finances under control,” Branstad said.