President Donald Trump is the head of the Republican Party. Can Republicans make people ignore that?

That could be an issue next year, when Republicans hope to retain their critical majorities in both the House and the Senate. While candidates want to present a united GOP message and capitalize on Trump’s anti-establishment appeal, they do not want to be associated with what they see as a too-tame response to the white supremacism on display in Charlottesville over the weekend.

“There’s no mileage in denouncing the president of your own party,” says longtime GOP pollster Whit Ayres. “But you don’t want your race to become a referendum on your party’s president” either, he says.

Trump, a former Democrat, has been warring with his own party’s members of Congress, whom the president blames for failing to get his agenda approved.

But Trump’s initial response to the Charlottesville events, in which he failed to single out white supremacists for the hate and violence, blaming “many sides” for the deadly events, hit a nerve among Republicans – even those who have refrained from going after Trump in his first seven months in office. The president’s tepid response was especially jarring to lawmakers who just watched their president single out Senate Majority Leader Mitch McConnell, R-Ky., for the president’s stalled agenda on the Hill.

“We should call evil by its name. My brother didn't give his life fighting Hitler for Nazi ideas to go unchallenged here at home,” GOP Utah Sen. Orrin Hatch, president of the Senate, tweeted in an apparent reference to Trump’s failure to be more direct in denouncing the movement represented by the Charlottesville demonstrators. In another tweet, the usually non-confrontational Hatch added, “Their tiki torches may be fueled by citronella but their ideas are fueled by hate, & have no place in civil society.”

Sen. Marco Rubio, a Florida Republican who was deeply critical of Trump during the campaign but more acquiescent once Trump was in power, pushed back as well. “Very important for the nation to hear @potus describe events in #Charlottesville for what they are, a terror attack by #whitesupremacists,” Rubio tweeted. And Colorado GOP Sen. Cory Gardner directed his Twitter comments directly at his party’s most senior member, saying, “Mr. President – we must call evil by its name. These were white supremacists and this was domestic terrorism.”

The White House sought to regroup after the onslaught of criticism, but still muddied the political waters by casting the criticism as an attack not on hate itself, but on the president personally.

Vice President Mike Pence on Sunday bluntly said that “we will not tolerate hatred and violence of groups like white supremacists, the KKK and neo-Nazis. These extremist fringe groups have no place in the American debate.” But Pence then expanded his disappointment to include the media, which he complained have “spent an awful lot of time focusing on what the president said and criticisms of what the president said instead of criticizing those who brought that hatred and violence to the streets of Charlottesville, Virginia.”

Then, on Monday, following the barrage of criticism, Trump gave brief remarks at the White House Monday to condemn racism. "Racism is evil, and those who cause violence in its name are criminals and thugs, including the KKK, Neo-Nazis, white supremacists," Trump said. But he did not explicitly reject the support of white supremacists or call it an act of domestic terrorism, as some lawmakers in both parties have urged him to do.

Meanwhile, Trump’s re-election campaign released an ad blaming the “enemies” of his administration for obstructing his agenda. The enemies? Democrats, career politicians and the media.

That messaging worked well for Trump in 2016, who ran on an anti-establishment platform.

The difficulty, Ayres says, is in not letting the president define the entire party, or even the campaigns of individual Republicans.

“Traditionally, a president of a party defines what that party stands for, but this is a unique president and we’re going to see if the party actually gets defined by him when so many other Republican voices are saying something very different,” Ayres says.

Republicans can indeed separate themselves from Trump’s response, says veteran Pennsylvania political observer Jon Delano, since Trump has never really been an embodiment of the party itself. Trump won Pennsylvania (and Wisconsin, Ohio and Michigan) by tapping the economic and cultural frustration of white, largely male, voters, Delano notes. But other GOPers can still denounce what happened in Charlottesville – and even denounce the president for responding too timidly – without turning off that Republican-friendly bloc, says Delano, an adjunct professor at Carnegie Mellon University.

“Certainly, there are plenty of white, working class males who feel that minority races get all the breaks and they don’t. But that doesn’t make them racist for feeling that way or voicing that sentiment,” Delano says. “It’s one thing to stand up for white, working class Americans who have been pilloried by this economy, haven’t seen their wages grow, lost their job to foreign trade or what they perceive to be unfair environmental [regulations] on one hand. But defending outrageous racist conduct” is something else, he says.