As majority whip, John Cornyn has tangled often with the tea party. He has championed pragmatic floor tactics and was an architect of the GOP’s successful drive to broaden its Senate footprint over the last three cycles by betting on candidates with establishment roots. He handily defeated seven gadfly challengers in a 2014 primary election.

Now, in the 114th Congress, the 63-year-old Cornyn has emerged in a new role as a conservative lion at the center of a bitter feud over abortion. When Democrats attacked Cornyn’s anti-human trafficking bill for including a permanent ban on the use of money in a trafficking victims fund for abortion, Cornyn became the frontman for the GOP’s case. He played much the same role in the fracas over executive orders on immigration in the homeland security spending bill.

For Cornyn, it effectively marks the opening act in a tryout to eventually succeed Majority Leader Mitch McConnell of Kentucky, 73, who would face re-election in 2020. Coming floor battles — including potential deals on less contentious domestic priorities — will provide a showcase for skills he must master in order to survive a three-term limit he faces as whip in 2019.

Cornyn’s emergence as an anti-abortion champion represents part of his effort to mend fences with the right wing and increase his standing as a successor to McConnell, the only elected GOP leader without a term limit.

“If you’re playing the long game, this is exactly the move that you make,” says John J. Pitney Jr., a political scientist at Claremont McKenna College in California. “It makes you acceptable to social conservatives, without making you radioactive to the general public.”

While shying away from divisive fights on gay marriage and marijuana legalization, Republican leaders face pressure from social conservative activists emboldened by a slight erosion in public support for unfettered abortion access.

In an interview, Cornyn portrayed his tactics on abortion as part of the ebb-and-flow of moving bills, and not aimed at scoring political points in the GOP. To remain a party leader, he says: “I think you earn the trust and confidence of your colleagues. And that’s very important.”

That’s why Cornyn rushed to the floor on March 18 when Democrat Dianne Feinstein demanded deletion of the permanent abortion funding ban and took a jab at GOP staff work on the bill. “There seems to be a ship passing in the night. It seems to be me,” Cornyn said during an emotional colloquy.

Among fellow conservatives, the squabble has been a Cornyn coup. Douglas Johnson, top lobbyist for the National Right to Life Committee, an anti-abortion group, praised Cornyn’s “refusal to be bullied.”

But Cal Jillson, a political science professor at Southern Methodist University, predicts the feud could be a double-edged sword, because of the potential ripple effects of launching an early round of abortion wars in a deeply divided Congress, with a limited window of opportunity for finishing bills before the full-blown onset of the presidential campaign season.

“It doesn’t look savvy to me,” Jillson says. “The theme presented by McConnell and Cornyn was that Republicans would show the Senate worked and ensure that everyone was treated fairly. Putting that provision in the trafficking bill has ground the Senate to a halt.”

Cornyn and McConnell have replied to such criticism by making clear that they will continue to take a tough line on abortion, including a vote promised by McConnell on a proposal to ban such procedures after 20 weeks. But Cornyn says they also intend to keep making progress on other items on the GOP domestic agenda and will keep those separate from abortion fights and veto face-offs with President Barack Obama.

“I’m for fighting the good fight to the bitter end, where we have a reasonable chance of success,” Cornyn says. “But where we are guaranteed to fail, I don’t believe in embracing bad tactics.”

McConnell praises his top lieutenant, to whom he appears to be granting a wide-ranging and visible role, as a “vital member” of his team.

“I count on him every day, not only to know how members will vote, but to help manage both our conference and the important issues that come before the Senate,” he said in a written statement.

Cornyn has worked behind the scenes with McConnell to build coalitions for must-pass bills such as a debt-limit increase and spending bills without poison-pill add-ons to repeal the health care law or reverse Obama’s executive action to defer deportations. And he has worked closely with committee chairmen and other key players such as Democratic Sen. Charles E. Schumer of New York, who sits with him on Judiciary and Finance, to fashion deals on a number of modest bills.

Such items, if enacted, could help to make up for potential stalemates on other high-profile goals such as a tax overhaul, tweaks to the health care law and a blueprint for new immigration rules, which Cornyn says must proceed “step by step” with small bills, rather than with a comprehensive measure.

In Schumer, Cornyn has found both a rival and an occasional partner on legislation and in exercise workouts. Cornyn says he recently welcomed Schumer, the anointed successor to Minority Leader Harry Reid of Nevada, to the Senate gym with a bow and a greeting: “All hail.”

“It’s a little premature,” Schumer replied, according to Cornyn.

The second-ranking Republican describes his future Democratic floor leader as “someone I can do business with,” and who is “riding the tiger” in a more liberal Democratic caucus after the 2014 losses by several red-state Democrats.

A former state Supreme Court justice and attorney general in Texas, Cornyn has earned a reputation as a well-informed lawyer and an even-handed jurist, with a penchant at times for tough tactics.

“He’s from Texas. He’s strong,” says his Democratic counterpart, Richard J. Durbin of Illinois.

In recent days, Cornyn has worked with Judiciary Chairman Charles E. Grassley of Iowa, and the panel’s ranking Democrat, Patrick J. Leahy of Vermont, to try to revive a shared draft bill from the last Congress aimed at deterring patent infringement lawsuits based on frivolous, or unreasonable, claims. And Cornyn has worked with another liberal, Sheldon Whitehouse of Rhode Island, on a bill aimed at easing prison crowding by offering inmates in rehabilitation programs a shot at early release.

With an eye on bipartisan bills that can be signed into law — or used to set up veto override votes and campaign themes — Cornyn has worked to keep Republicans unified and has opened his door to consultations with swing Democrats such as Joe Manchin III of West Virginia. While seeking their votes, Cornyn says he can sometimes offer openings for floor votes on their amendments.

By allowing for ample floor votes and working at times with Democrats, Cornyn argues that occasional fights on abortion and other issues will not harm GOP efforts to complete a number of near-term priorities, noting the Senate just cleared a bill averting perennially scheduled cuts in Medicare reimbursements for physicians. Next up: granting Trade Promotion Authority to Obama and a measure to provide for review by Congress of the nuclear deal with Iran.

“A couple months from now, I think we will look back and say that was a pretty remarkable run of bipartisan accomplishment,” Cornyn says.

The completion of such bills could help the GOP to weather a potential storm in the 2016 elections. With Democrats already favored to gain ground — 24 GOP-held Senate seats are at risk — most Republicans say that McConnell and Cornyn likely will get considerable slack, whatever happens.

Barring unforeseen GOP setbacks, Cornyn could be set after the 2016 election to continue in his role as a moral conservative champion and to make a strong case for retention in the leadership when he hits a term limit at the end of the next Congress.

At that point, Cornyn and a number of other party leaders would be staring at looming term limits. Among the leaders that could be facing three-term limits are several potential Cornyn rivals: John Thune of South Dakota, 54, the Republican Conference chairman; John Barrasso of Wyoming, 62, the Republican Policy Committee chairman, and Roy Blunt of Missouri, 65, the Republican Conference vice chairman.

Diplomatically, Cornyn has been careful to stay away from the GOP presidential sweepstakes, unlike McConnell, who is backing home-state ally Rand Paul. In defending his unaligned stance, Cornyn cites conflicting ties to two Lone Star State giants, Sen. Ted Cruz and former Gov. Rick Perry, and two native sons, Paul and former Florida Gov. Jeb Bush.

Colleagues say that Cornyn’s popularity in his caucus likely could help him to keep a place high on the ladder, perhaps by securing a term-limit waiver or an alternative perch, meaning he could stay in the race to eventually be the top Republican.