CLEVELAND — Speaking to Iowa Republicans here on Monday, Gov. Scott Walker of Wisconsin repeatedly reminded them of his childhood in the state that kicks off the presidential nominating process. Before the same crowd on Tuesday, Senator Tom Cotton of Arkansas had his own boast. “I’m the only politician here this week that married a girl born in Iowa,” said Mr. Cotton, admitting it was a “pander.”

Bruised by their indecorous primary, which left some of the party’s brightest stars reduced to wounded pets on the side of the road and pessimistic about taking over the White House in November, many Republicans are quietly turning their focus to 2020.

Jockeying for future presidential campaigns is a feature of every party convention, and the Republican meeting in Cleveland this week is no exception. But the subtle wooing and chit collecting have taken on a new air of urgency this year, with many party leaders openly skeptical about whether Donald J. Trump can defeat Hillary Clinton.

Mr. Trump’s ascendance has shown that Republican voters craved alternatives to conventional candidates from governor’s mansions and Congress.

But that is not stopping a conventional array of aspirants from lining up once again. The roster of potential 2020 candidates includes several of this year’s primary losers, including Senators Ted Cruz of Texas and Marco Rubio of Florida, Gov. John Kasich of Ohio and Mr. Walker, as well as younger hopefuls like Mr. Cotton.

They calculate that the experiment with Mr. Trump, if he loses, will trigger buyer’s remorse within the party. The next nominee will be well positioned, they estimate, because the electorate will be ready for change after three consecutive Democratic terms in the White House.

“If you thought this year was an attractive race on our side, imagine 2020,” said Phil Cox, a former executive director at the Republican Governors Association. “You’ll have 30 people running.”

Mr. Cotton and Mr. Walker are visiting the delegations from all three of the traditional early nominating states — Iowa, New Hampshire and South Carolina — and Mr. Kasich is rekindling ties with the New Hampshire delegates. Each of the prospects has also been racing through Cleveland’s heavily secured streets to court major donors like Las Vegas casino magnate Sheldon Adelson.

For now, much of the positioning is going on relatively quietly. Yet potential candidates are already making moves to help pave their paths. Most obvious is Mr. Cruz, who has landed a prime speaking spot at the convention despite several nasty scrapes this year with Mr. Trump.

Mr. Cruz has created two nonprofits to serve his political ambitions and maintain his donor database. He has also installed a veteran political operative who worked on his campaign as his new chief of staff, a move the senator’s associates said was done to make the office less a miniature think tank and more a presidential incubator.

And his political allies, including Senator Mike Lee of Utah, staged an insurrection on the convention floor on Monday as part of a failed attempt to change party rules that would have been more advantageous for Mr. Cruz’s future political ambitions (one of the changes: mandating that only registered Republicans can participate in presidential caucuses and primaries).

Mr. Cruz has been aggressively pushing legislation that would help his political agenda, including a recent bill that would place mandatory minimum sentences on illegal immigrants who return to the country.

“My focus now is fighting for the very same conservative principles in the United States Senate that were at the heart of our presidential campaign,” Mr. Cruz said.

Mr. Cotton, 39, is also trying to seduce early-state Republicans while playing nice with his colleagues.

He was the keynote speaker in March at the Silver Elephant Dinner for rising stars among South Carolina Republicans, and he won a speaking role at the Iowa Economic Forum lunch with convention delegates here.

Mr. Cotton was one of five freshman senators who traveled to Arizona in support of Senator John McCain, who is facing a tough re-election fight there. He attended a Republican dinner in Missouri for Senator Roy Blunt, who is also in a tough race.

In August, Mr. Cotton will travel the country, including a stop in Nevada to campaign for Representative Joe Heck, a Republican, who is running for the seat being vacated by Senator Harry Reid, the minority leader.

Like Mr. Cruz, Mr. Cotton is attempting to establish himself on the right flank of the potential primary field over one of the most galvanizing issues among conservative activists. “I think the fact of the matter is that right now, we have too much immigration,” Mr. Cotton said.

Mr. Rubio decided to run for his Senate seat in Florida after repeatedly denying that he would. But his colleagues have noted that he has become far more engaged in Senate business over the past few months than over the past two years, taking the lead on fighting for funding for combating the Zika virus, for example.

For his part, Mr. Kasich is making the most of his home-state convention, though he is not scheduled to speak. With the governor under attack by Mr. Trump’s campaign for not endorsing the party’s standard-bearer, allies of Mr. Kasich struck back aggressively in a way that could well position him for the future with the many Trump skeptics in the party’s ranks.

Mr. Kasich has been ubiquitous this week. He addressed the N.A.A.C.P. in Cincinnati and appeared at fund-raising events in Cleveland for the committees dedicated to electing Republican governors, House members and senators. He will also appear at a foreign policy seminar and a Hispanic Chamber of Commerce event.

Bridging the gap between the hard-right wing of the party and the pragmatists is the House speaker and convention chairman, Paul D. Ryan, whom many Republicans tried to lure into challenging Mr. Trump at the convention.

Mr. Ryan has threaded the needle by supporting Mr. Trump while also openly disagreeing with him on some issues. But he will soon be pressed about whether he intends to make a career of the speakership or position himself for a presidential bid if Democrats take the White House and Senate.

As the speaker, he has a natural friend-making apparatus in his fund-raising operations. Since he became the speaker, his political organization has raised nearly $38 million, with more than $25 million used to help re-elect House Republicans. His campaign committee, Ryan for Congress, has $9.75 million in cash on hand, the most for any member of the House.

This month, he will have an opportunity to swell those coffers and make new friends for a future presidential run when he appears at the Koch organization’s summer gathering at the Broadmoor resort in Colorado.

Mr. Ryan left little doubt about how he wanted to rebrand the party should Mr. Trump lose.

“The Republican Party is a ship floating on populism right now,” Mr. Ryan said. He criticized those who “profit off anger, outrage and dark emotions for short-term goals.”

Gaming out policy implications, let alone promising candidates, can be folly in volatile political times. After all, few in the party at the last convention could have ever imagined Mr. Trump emerging as their nominee in 2016. And should he fall short in November, his example may only inspire a cast of imitators four years from now.

“Are there more Mark Cubans out there who say, ‘Well, this is easy, and I’m not a nut, so I may even be successful’?” said Dave Carney, a longtime Republican strategist, referring to the wealthy Dallas Mavericks owner and ubiquitous media presence. “Trump has given them a road map.”