After yet another primary loss for Hillary Clinton — this one on Tuesday in West Virginia — Republican National Committee Chairman Reince Priebus decided to have a little fun at the Democratic frontrunner's expense.

Sick Bern! And indeed, Clinton has lost an embarrassingly large number of times — Priebus is right, it's 20 and counting — to Bernie Sanders. But the sardonic responses were predictably quick. Priebus soon heard from people demanding to know whether he was embarrassed by presumptive GOP nominee Donald Trump, enumerating his myriad sins.

That's social media for you. But what was more unusual is how much of the blowback came from conservatives, including people working in conservative media.

Donald Trump has a conservative media problem. National Review has been standing athwart the billionaire yelling stop since last year. The Weekly Standard's editor has been searching for a third-party alternative to Trump, even if it takes pulling Mitt Romney out of mothballs. From long-established magazine editors to twenty-something staff writers, from widely syndicated columnists to up-and-coming bloggers, Trump is brutally unpopular among conservative journalists.

Of course, none of this has prevented Trump from all but wrapping up the Republican presidential nomination or suddenly polling competitively with Clinton in key swing states. Conservative elite influence is often exaggerated. (There was no President John Ashbrook, for example.) But the influence of conservative elites isn't nonexistent either. And their opposition to the presumptive GOP nominee could hobble Trump in the general election.

Consider the recent reports that Trump was flip-flopping on taxes. When the probable Republican nominee suggested that in reality the wealthy would have to pay a little bit more than he suggested in his tax plan, anti-Trump conservatives pounced: See, Trump the liberal has reemerged even before the GOP convention! He's a RINO, not a true conservative!

If Trump was a normal Republican, conservative media would have taken the lead in contesting the flip-flopping charges. Instead, it was liberal outlets whose readers might prefer higher taxes on the wealthy who did the most pushing back, while conservative outlets were among the quickest to echo the flip-flopper charge.

When news breaks that is superficially bad for Trump, conservative reporters are now as likely as — maybe more likely than! — liberal reporters to immediately to treat the bad-for-Trump news credulously rather than skeptically.

Lots of times, this may be the right way for everyone to react to Trump controversies. But it's not the way conservatives would have treated nominees from Reagan to Romney. And while the influence of conservative elites is often overstated, their fierce opposition to Trump will absolutely affect the way Trump is perceived over the course of the campaign.

With a different nominee, potentially even including some of Trump's rivals in this year's primaries, House Speaker Paul Ryan would be regarded as a traitor for refusing to immediately endorse. Ryan would get the Chuck Hagel treatment. Instead Ryan is the hero in this morality tale and Trump is the goat.

Certainly, Ryan has a longer and more consistent record of articulating and defending conservative principles than Trump. But if you define conservatism more like many rank-and-file conservative voters do and less like the average conservative journalist, where support for immigration restriction is arguably a higher priority than capital gains tax cuts, there's a case to be made for Trump over Ryan.

Good luck hearing that case in leading conservative publications.

Similarly, when Romney suggests there might be something untoward in Trump's taxes, the conservative press is not going to treat him like Harry Reid.

If a semi-credible third-party candidate does emerge, he or she is going to get a lot of coverage in the conservative press, especially initially. There's no guarantee that will siphon many votes from Trump. But it only took 2.7 percent of the vote for Ralph Nader to tip the extremely close 2000 race.

Do not cry for the Donald. Trump will have his reflexive defenders on the right, some of whom have will have bigger audiences and wider reach than the smaller magazines and periodicals arrayed against him. He also can get better earned mainstream media coverage than many other Republicans, largely due to his celebrity status.

Conservative media nevertheless helps keep the marketplace of ideas somewhat "fair and balanced," as the old Fox News slogan says. But Trump is going to have detractors on both sides singing from the same song sheet.

There will be times where that might be to journalism's benefit. It just isn't helpful to Trump.