Republican Party chairman Reince Priebus speaking at a campaign rally for Donald Trump in Everett, Wash. (Carlo Allegri/Reuters)

Donald Trump has recently seen a surge of support in national and state polls. But a considerable number of Republicans still refuse to support him. On CBS’s Face the Nation on Sunday, Republican National Committee Chairman Reince Priebus warned them: Support Trump now, or face the RNC’s wrath later.

But what can the RNC actually do to punish Republicans who refuse to endorse Trump? The answer, as I’ll explain, is not much.

Who are the Republicans who’ve refused to support Trump?

As Jeff Jenkins and I have explained, politicians usually endorse their party’s presidential nominee — even if they have strong disagreements on specific issues. And Trump’s primary opponents all pledged they would support the Republican nominee in the general election.

But a number of top Republicans still oppose Trump. These holdouts come in three categories.

1. Republicans who are on the ballot this year

At least 13 Republican elected officials and candidates who are running for office this year have refused to support Trump. Many fear he will lose in November and will drag them down, too. For example, Senators Mark Kirk of Illinois, facing a close reelection battle, has explicitly said he will not vote for Trump.*

2. Republican former officeholders

Some former elected officials and officeholders no longer active in politics feel free to criticize Trump. These include former presidents George H.W. Bush and George W. Bush, and 2012 presidential nominee Mitt Romney.

3. Republican 2016 primary candidates

Four 2016 presidential primary candidates — Jeb Bush, Ted Cruz, Lindsay Graham and John Kasich — still refuse to back Trump in the general election. Bush announced he would not vote for either Trump or Clinton in July. Cruz did appear at the Republican National Convention, but he refused to endorse Trump, telling Republicans to “vote your conscience.” Kasich last week said it was “very unlikely” that he would vote for Trump.

Although Bush, Cruz, Graham and Kasich are not on the ballot this year, they could run again in 2020 if Trump loses to Clinton. In his Face the Nation appearance, Priebus argued that since these former presidential candidates “took part in our process, they used tools from the RNC” and “agreed to support the nominee” — they now “need to get on board.”

Crucially, Priebus also warned them that a failure to do so would hurt them in future races, adding, “if they’re thinking they’re going to run again someday, I think that we’re going to evaluate the process — of the nomination process and I don’t think it’s going to be that easy for them.”

The RNC doesn’t have a lot of tools for punishing individual Republicans.

But threats are easy. In reality, national committees cannot do very much to punish individual politicians for failing to support a presidential candidate.

The national committees do try to influence their parties by pushing them in certain policy or ideological directions, and to confront Republican factions that resist. In particular, the DNC and RNC do so through their role of publicizing party positions. But political parties cannot easily constrain individual candidates in the American political system.

Most important, the national committees don’t control ballot access or party membership. That means the RNC cannot ban individual candidates from running in Republican primaries or from appearing as the Republican nominee on the ballot. If someone wins a GOP primary, he or she will appear on the general election ballot as a Republican.

So what tools do national parties actually have to punish “disloyal” members?

1. Kicking someone out of the caucus

One approach is for congressional Democrats or Republicans to refuse to allow individual members to caucus with the party. The RNC would have no say on this. Even if it did, that wouldn’t affect someone like Kasich (who’s a governor and not up for reelection) or Bush (who’s not currently in elected office at all).

What’s more, such ostracism is rare. Even Strom Thurmond — who as Democratic governor of South Carolina ran as a Dixiecrat presidential candidate against Democratic president Harry Truman in 1948 — still caucused with Democrats after being elected to the Senate in 1954, until he switched to the GOP in 1964. And in 2008, Joe Lieberman — a former Democrat who won the 2006 Connecticut Senate election as an independent, but kept caucusing with the Democrats — supported John McCain. Senate Democrats didn’t strip Lieberman’s committee chairmanship, fearing he would join the GOP instead.

2. Reducing a state’s delegates to the party’s convention

The national committees do have a powerful tool to force compliance: Cut the number of a state’s national convention delegates.

The committees have often done so in the past. For example, in 2008, Michigan Democrats held a primary earlier than the DNC had prescribed. As punishment, the DNC reduced the number of delegates the state could send to the 2008 Democratic convention.

But that’s only effective when the national committee wants to punish the state party organization. It’s hard to imagine that, to punish Cruz or Kasich, the RNC would cut Texas or Ohio’s delegations.

3. Withholding support in a general election

The party committees do support candidates with services such as campaign donations, data and resources, advice, and staff. In theory, they could withhold such support from people like Graham, Kasich or Cruz in future elections. But in practice, this seems very unlikely. Would the RNC risk losing to Democrats just to punish individual Republicans for not supporting Trump in 2016?

4. Excluding candidates from RNC services during primaries

The RNC generally stays out of primaries but it does have some ways to influence presidential primaries.

First, it could exclude “disloyal” candidates from future presidential primary debates. As Julia Azari and Seth Masket have shown, the national committees have recently become involved in organizing primary debates. The RNC could theoretically ban “disloyal” Republicans from future debates.

Second, the RNC could refuse to let particular candidates use its voter data, usually available to all candidates in the primaries. That would deny them a wealth of information on potential voters and how to reach out to them.

But would the RNC actually do either?

If Trump loses, the GOP will have lost three presidential elections in a row for the first time since 1942. The party will be under a lot of pressure to win in 2020. It seems very unlikely that the RNC would constrain viable candidates because they rebelled against Trump’s 2016 candidacy. And none of this applies to former officeholders who won’t be running again.

The RNC is in a weak position when it comes to policing individual party members: It either can’t or won’t use its tools to force cooperation.

Of course, opposition to Trump may have consequences for Republicans: His voting base may not forgive and forget, and may punish the holdouts at the ballot box.

But Priebus’s comments this weekend are empty threats.

Boris Heersink is a PhD candidate at the Woodrow Wilson Department of Politics at the University of Virginia.

*Correction: An earlier version of this post incorrectly asserted that Sen. Susan Collins was up for reelection. She is not up for reelection until 2020. We regret the error.