Conservatives, still reeling over the looming nomination of Donald Trump, are pushing new Republican primary rules that might have prevented the mogul’s victory in the first place: shutting out independents and Democrats from helping to pick the GOP nominee.

Trump romped in “open primaries” where non-Republicans voted by the thousands and may have influenced the outcome — especially in early states that set the tone of the entire race. Trump’s most successful rival, Ted Cruz, thrived in states with closed primaries where only Republicans were permitted to participate.

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Now, Cruz’s allies — hundreds of supportive convention delegates that he helped elect — hope to use the national convention in Cleveland to shove states toward closing their open primaries. And if they’re successful, it will not only go a long way toward warding off a Trump-like candidacy, it will tilt the primary toward conservative candidates in 2020 and beyond.

The advocates are finding a sympathetic ear at the very top of the party. Republican National Committee Chairman Reince Priebus has long supported closed primaries, but has never had a constituency to back him on it. "I believe that only Republicans should vote in Republican primaries," he said Friday at a Politico Playbook breakfast event, though he added that he respects the right of states to set their own primary rules.

For the conservatives, Trump’s path through the Republican primary is proof that the system needs to change.

“We now have a progressive, Trojan horse candidate that manipulated the open primary process to hijack the GOP nomination,” said Kendal Unruh, a Colorado GOP activist, said of Trump. Unruh will sit on the Convention Rules Committee, the panel that will set the terms for the 2020 presidential campaign.

Cruz himself is at the forefront of the effort, and he has continued pleading with his delegates to battle their way to the convention and commandeer the rulemaking process that will govern both the July convention and the 2020 presidential election process. In a conference call with his delegates Monday night, Cruz and top campaign adviser Ken Cuccinelli urged them to fight for rules that enhance the power of the party’s grass roots. Choking off Democratic and independent influence from primaries is one way to do that, said Unruh, who was on the call.

“We still have a job to do,” she said.

Unruh isn’t alone. Her fellow Rules Committee member from Colorado, Guy Short, ripped open primaries as antithetical to GOP interests. “I think we need to start punishing states that have open primaries,” he said. “If you’re not a Republican, then you can wait for the general. Democrats shouldn’t have a role in choosing our nominee.”

For years, these arguments have hit resistance from GOP elders and the party insiders who controlled the rulemaking process at conventions past. Closed primaries, they say, are self-defeating; shutting out non-Republicans shrinks the pool of engaged voters and limits the party’s ability to attract new support.

But Cruz’s unrivaled organizing and lengthy candidacy helped him recruit hundreds of supportive delegates, and that could upend the calculus and predictability of the process this year. Many are still sore over Trump’s win and wouldn’t mind crossing the presumptive GOP nominee, who now views himself as the leader of the party.

“I don’t believe they would be concerned that it would be a slap at Donald Trump,” said one Republican delegate to Cleveland, who also served on the Convention Rules Committee in 2012.

A move toward closed primaries would dramatically shift the way the Republican Party chooses its leader. Most states have open primaries or hybrid systems — from permitting crossover voting, to allowing voters to register on-site, while some have no party-based registration at all. Only about a dozen states have closed GOP primaries.

Opponents of open primaries are particularly concerned about their prevalence early in the nominating calendar. After losing Iowa’s caucuses, which are only open to registered Republicans, Trump beat rivals in New Hampshire and South Carolina, where Democrats and independents are permitted to cast “crossover” votes. Those victories branded Trump as the candidate to beat and knocked out several other candidates, including Rand Paul, Carly Fiorina and Jeb Bush.

Opponents of open primaries are floating a variety of proposals that would shift the balance of power toward states that restrict participation to Republicans. One, which failed at the 2012 convention, would reward closed-primary states with extra convention delegates, enhancing their power over the presidential nominating process. Another would force more closed-primary states to the front of the GOP nominating calendar, ensuring that the early leader of the contest has more GOP buy-in.

Supporters of closed primaries say it’s only logical that Republicans get to choose the Republican presidential nominee. Oklahoma GOP Chairwoman Pam Pollard, whose state held the first closed contest of the primary season this year, said open primaries are like inviting the opposing football team to choose your team’s quarterback. Pollard, as a party chair, will be an automatic delegate to the national convention.

Some say, however, that the decision should be left to the states, rather than set via a national standard.

Rod Lamkey Jr. for POLITICO

“Wherever possible, power should flow from the bottom up rather than the top down,” said Morton Blackwell, a Virginia delegate and veteran RNC committeeman. Blackwell supports closed primaries and is pushing for one in Virginia, but he would oppose any effort to force all states to do the same.

In 2012, the convention Rules Committee debated a proposal that was even less radical: rewarding states that choose to hold closed primaries with a 10 percent increase in delegates. But that effort, too, was shot down as too coercive.

“Isn’t one of our goals of the party to increase our voter registration?” Kurt Criss, Nevada’s Rules Committee member in 2012, argued at the time. “But where do we think these voters come from? They come from other parties.”

Henry Barbour, Mississippi’s RNC committeeman and a 2012 Rules Committee member, said at the time “We’re a bottom-up party. And the last thing that we need is the national party trying to tell us … how we’ve got to run our primaries.”

If the push for closed primaries fails in 2016, one factor may be the acute fear of appearing to cross Trump, whose dominance in open primaries was a storyline of the campaign. Though he had a handful of victories in closed contests — most notably Nevada’s caucuses, as well as primaries in Arizona and New York — open primaries were where he thrived.

“I probably would not advocate for it at this convention,” said Pollard, the Oklahoma GOP chairwoman, a staunch supporter of closed primaries. “I don’t want anyone to think that this issue has anything to do with Trump versus Cruz versus Rubio or anybody else. Things are so sensitive right now.”

Pollard added that she hopes the RNC considers rule changes after the convention, when Trump is almost certain to be the official nominee and passions among his Republican opponents may subside. She argues that the ability of the rapid-fire news cycle to winnow the GOP field after just a few early-state contests makes it more pressing than ever to push closed primary states to the front of the calendar.

“Forty percent of our candidates dropped out by the fifth primary,” she said. “As Republicans, we do strongly believe in states’ rights. But I think you also need to look at the overall consequences of some of our rules.”