It was October 1998, and Hillary Clinton’s midterm campaign swing for Democratic candidates brought the first lady on a Saturday afternoon to a middle-school gymnasium in Janesville, Wis. A 28-year-old conservative upstart from the town was running for Congress — and Clinton, rallying 1,200 people with a rip-roaring denunciation of Republicans, was trying to stop him.

Clinton’s efforts failed, of course. Paul D. Ryan went on to win, and he has held his House seat in Wisconsin’s industrial southeastern corner for nearly two decades as he has risen to become the highest-ranking Republican in the country.

Clinton and Ryan did not know each other then, and they barely have a personal rapport now. When they served together on Capitol Hill, they did not collaborate. They have crossed paths only a few times, in perfunctory meetings while she was secretary of state. Clinton, 68, and Ryan, 47, also have no apparent social ties — although they do share a book agent, Washington super-lawyer Robert Barnett.

Nonetheless, their relationship could become Washington’s most important in determining whether the federal government functions over the next four years, should Clinton win the presidency and Ryan retain his majority — as polls show is probable, although not certain, for both.

Ryan’s uneasy relationship with Republican presidential nominee Donald Trump — one that appeared to reach its breaking point this week — has been front and center in this year’s melodrama of a campaign. It’s less clear what a Clinton-Ryan relationship would look like.

House Speaker Paul Ryan said on July 6 that Democratic presidential candidate Hillary Clinton may have been given preferential treatment from the FBI in its investigation of her use of a private email server and should not receive classified information during her campaign. (Reuters)

“It’s fine,” Ryan said flatly when asked about his relationship with Clinton at a late-September breakfast hosted by the Economic Club of Washington. “I’ve only had two or three conversations with her. . . . I can’t really say I know her very well.”

The relationship would hinge on how Clinton decides to begin her presidency. She could claim an electoral mandate and launch a pitched battle to pass the more progressive parts of her agenda. Or she could start with a relatively incremental push on a menu of domestic issues on which she and Ryan have shared interests, including infrastructure investment, criminal-justice issues and anti-poverty measures.

“Do they want to begin it at loggerheads or with some signal to a very frustrated electorate that there is ground to be gained by focusing on the overlap between their two agendas?” asked William A. Galston, an official in President Bill Clinton’s administration and a senior fellow at the Brookings Institution.

Mixed views about partnership

There is a glaring fault line between optimism and pessimism about Clinton and Ryan forging a productive partnership. Some see the pair as policy wonks with pragmatic instincts who are poised to break the logjam. Others say their political caution and entrenched ideologies would prevent them from defying their bases to resolve disputes and build agreements.

“To assume Washington is going to work next year is to assume she’s not Clinton and he’s not Ryan,” said former House speaker Newt Gingrich (R-Ga.), who has been advising Trump and had made legislative pacts with Bill Clinton on issues such as welfare and spending.

“Paul Ryan will not be dealing with Bill Clinton,” Gingrich said. “I had a guy I could talk to who had been the governor of Arkansas and dealt with that state’s legislature and helped to found a centrist organization,” he added, referring to the Democratic Leadership Council. “Hillary, on the other hand, is someone who is hard left. They are totally different people with different instincts.”

The other power broker in the Clinton-Gingrich negotiations, Republican former Senate leader Trent Lott (Miss.), has a far different assessment.

Donald Trump started attacking members of his own party in a series of tweets Tuesday after many Republicans rescinded their support for the presidential nominee. The Fix's Chris Cillizza weighs in on the unprecedented unraveling of the GOP. (Jayne Orenstein/The Washington Post)

Lott pointed to the lessons Hillary Clinton took away from watching her husband negotiate with Congress, as well as the warm relationships she built with Lott and other Republicans when she served in the Senate. He said Ryan has an even temperament and eagerness to shed his party’s reputation as obstructionist, as evidenced by the budget deal he struck with Sen. Patty Murray (D-Wash.) in late 2013.

“Paul Ryan’s nature is to try and find a way to make things work,” Lott said. “And Hillary has seen how important communication is. She understands they’re not just a bunch of rogues up there. . . . You’ve got to be willing to give a little to get a little. That’s how Bill Clinton and I made deals across the board.”

Ryan’s biggest obstacle to partnering with Hillary Clinton would probably be the House Freedom Caucus, a group of dozens of hard-line conservatives whose threats of rebellion led Ryan’s predecessor, John A. Boehner (R-Ohio), to resign and who have become a thorn in Ryan’s side.

One member, Rep. Dave Brat (R-Va.), who ousted then-House Majority Leader Eric Cantor in a primary two years ago, vowed to work with Clinton on issues such as fighting terrorism, but he said, “I don’t see a love fest.”

“For us, it’s not about Paul Ryan,” Brat said. “It’s about constraining anyone who’s opposed to stopping the expansion of the federal government.”

House Republican leaders have said that if Clinton is elected, they intend to continue their investigation into her use of a private email server as secretary of state, forecasting a stormy atmosphere. “Next year could be very much like 1998, when we impeached Bill Clinton,” Gingrich said.

Rep. Chris Van Hollen (D-Md.), who worked with Ryan on the House Budget Committee, said “the jury is still out” on the prospects for common ground.

“The question for Paul Ryan is, is he going to be a speaker who wants to try and govern with President Clinton or continue to kowtow to the tea party faction?” Van Hollen said. “I think that battle within the Republican caucus is unavoidable. . . . If he wants to get stuff done, he’s going to have to be willing to have that showdown.”

On top of the possible tensions between the speaker and Clinton could be a Senate with a narrow majority, with Mitch McConnell (R-Ky.) or Charles E. Schumer (D-N.Y.) as majority leader, depending on election results this fall.

People who know Ryan said his amiable disposition can do only so much to help him connect with Clinton. “He’d be gracious and a gentleman, sure — less confrontational than Newt, and he’d be smoother than John Boehner,” said William J. Bennett, a close friend of Ryan’s and a former education secretary under President Ronald Reagan. But, Bennett said, “these aren’t people who are going out to dinner.”

Further complicating Ryan’s calculations could be his political ambitions — namely, whether Ryan, the GOP’s vice-presidential nominee in 2012, would try to position himself to run against Clinton in 2020.

Clinton probably would face similar pressures. She is distrusted by the Democratic Party’s liberal wing, which fueled the formidable primary challenge of Sen. Bernie Sanders (Vt.).

Sanders, Sen. Elizabeth Warren (D-Mass.) and their followers have signaled they would try to halt any move to the middle by a President Clinton on bedrock programs such as Social Security and Medicare, which Ryan has long targeted for sweeping changes.

Finding mutual goals?

For Republicans, Clinton presents potentially a far different negotiating partner than President Obama. Obama came to office with little record of bipartisanship and with a disdain for the social rituals that have historically greased relations at both ends of Pennsylvania Avenue. Clinton’s allies said she would be more sensitive to the political realities of divided government.

“One of my favorite expressions about leadership is, ‘The best way to persuade is with your ears,’ and she truly understands that — the need to listen,” said Democratic former Senate leader Thomas A. Daschle (S.D.).

Daschle led Senate Democrats through Clinton’s first four years in the chamber, and he recalled her painstakingly cultivating alliances across the aisle. For instance, she befriended Sen. Lindsey O. Graham (R-S.C.), who only a few years earlier had argued the impeachment case against her husband. They traveled together overseas and worked on issues such as military benefits. And in 2006, when Clinton appeared in Time’s “100 Most Influential People” issue, it was Graham who penned a glowing tribute.

“How do you build relationships?” Daschle asked. “It’s inclusion. It’s invitations to Camp David. It’s regular meetings at the White House. It’s socializing. It starts with that.”

In his failed attempts at a “grand bargain” with Boehner, Obama’s approach was to appeal to Boehner’s sense of reason and convince him that a deal was best for the country, even if he suffered a backlash on the far right. But Clinton’s associates said she would approach similar talks like a mechanic, understanding Ryan’s constraints and identifying areas of mutual advantage.

One such area could be an infrastructure spending bill, which Clinton has said would be an immediate priority. Ryan, too, has in the past year privately reached out to top Democrats about beginning infrastructure talks, which the U.S. Chamber of Commerce and other pillars of the Republican establishment have championed.

Clinton also would seek to work immediately on an overhaul of immigration law, an issue that Ryan has advocated but that has become anathema in parts of the Republican conference. It is possible that a Trump loss in November could shift political winds in the GOP, creating momentum for Ryan to consider starting discussions.

“It’s got to be done in stages and pieces, not some big, massive bill that ends up collapsing under its own weight,” Ryan said at the Economic Club about the prospect of an immigration pact next year.

There are other areas of mutual agreement, such as on criminal justice. Clinton and Ryan have expressed concern about mass incarceration and advocated changes to sentencing laws, and there are bipartisan efforts afoot.

Another issue is fighting poverty, something Clinton and Ryan prioritize, although they have clear disagreements on the solutions. Ryan sees it as his personal mission and thrust it to the forefront of the GOP policy agenda. His confidants said he would feel invested in reaching an anti-poverty accord with Clinton.

Bob Woodson, a veteran community organizer who has mentored Ryan, said he could envision Clinton and Ryan touring beleaguered urban neighborhoods together.

“Paul and I have taken many of these kinds of trips, and he does it in a way where politics isn’t part of it,” Woodson said. “It won’t be easy. She’s going to want more government; he’s going to want more choice in education and different ways of spending money to tackle these problems. But he’s the kind of person who could sit down and come up with five or six concrete steps where there is overlap.”

Clinton’s selection of Ken Salazar, a former Interior Department secretary and senator from Colorado, as co-chairman of her transition team was seen by some in Washington as a telling signal. “Ken was well known for his ability to work across the aisle,” Daschle said. “Just selecting Ken was a strong statement about her desire to govern.”

Ryan’s friends say a glimmer of hope may be the speaker’s aversion to the caustic animus toward the Clintons within his party’s ranks — a trait they say traces to his days as a staff member. The Midwesterner has never been comfortable about Clinton conspiracies or sordid accusations, despite his opposition to the Clintons’ policies.

“He wasn’t like a lot of conservatives his age in the ’90s who wanted to dig up Clinton dirt and scandals,” said Vin Weber, a former Minnesota congressman who worked with a just-out-of-college Ryan at Empower America, a think tank that has since shuttered. “Rather than talk about Monica Lewinsky, he’d want to crusade against tax increases.”

Ryan’s unease about Clinton barbs has been evident on the campaign trail and in private fundraisers, where he goes after her policies but not after her personally.

“He’s with his party, but he never said that he can’t work with her,” Weber said. “That’s a key distinction. He’s certainly not for her — but he has never said he’s unwilling to engage.”

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