CNN published an analysis of recent polls on Wednesday that might look terrifying for Democrats.

It showed Donald Trump trailing Hillary Clinton by just 2 points, drawing from several other polls recently that have put the two candidates neck and neck. Over the past two weeks, Quinnipiac said Trump is trailing by 4 points, Rasmussen said he's down by 2 points, and ABC News said Trump was in fact beating Clinton by 2 points.

This marks a major turnaround from months of polling that showed Clinton leading Trump by double digits through much of the primary season.

But the critical question is what this shift really means for the candidates' chances in November. We talked to five pollsters and three political scientists, and they all urged caution in reading too much into Clinton's apparent weakness while she continues to fend off a primary challenge from Bernie Sanders. But some of them also urged against dismissing the latest polls as meaningless statistical noise.

Less than a month ago, pundit wisdom held that Clinton would waltz to a historic landslide over Trump. It might be time to rethink that assumption.

Why these polls shouldn't scare Clinton

Trump is getting a post-primary bump, and Clinton probably will too: Jim Williams, analyst at the Democratic-leaning polling firm Public Policy Polling

Here's the silver lining for Clinton from Trump's polling rise: At least some of it is due to Sanders's fans growing less likely to say they'll support her in one-on-one matchups against Trump.

Of course, Clinton would prefer if that weren't the case. But it suggests she's sagging in part because of temporary — and presumably reconcilable — divisions among Democratic voters, rather than the movement of centrist independents away from her campaign.

In March, two-thirds of Sanders supporters said they'd support Clinton over Trump in a one-on-one general election contest. That number has since fallen to about 50 percent, according to YouGov polling.

"We're at the height of the animosity between Clinton and Sanders, and that explains some of this," Williams says. "This is when you're going to get people stomping their foot and saying, 'No, I'm not going with Hillary.'"

This syncs with the broader conventional wisdom right now: Trump is seeing a bump because he's won over initially skeptical Republican voters, and Clinton can likely expect a similar surge if Sanders drops out and endorses her.

"Once the Democratic nomination is decided, Hillary will further consolidate the party," Williams says. "Historically, with both parties there's a group of holdouts until when the primary campaign reaches its bitter end."

Polls this far out should mostly be ignored: Kathy Frankovic, former CBS polling director and analyst at YouGov; and Jonathan Ladd, professor at Georgetown University

Frankovic once tried keeping to a simple rule: Don't scrutinize general election polls until after Labor Day.

"Otherwise, you're spinning wheels — you're worrying or celebrating prematurely," she says. "You can look for signs and explanations as to why things are the way they are, but you have to be aware that you're looking at a lot of people who haven't decided yet."

This year, for instance, close to 20 percent of people still say that they haven't made up their mind between Clinton and Trump, according to Frankovic's latest YouGov poll.

That matches Ladd's view; he says we should be skeptical of any general election poll before the Democratic and Republican conventions are held in late July. (Princeton professor Sam Wang recently noted that general election polls are actually less predictive in the spring than they are in either February or August.)

"The political science conventional wisdom — which is not always right — is that the polls are much more correlated with the results after the conventions than before they're held," Ladd says. "The historical evidence shows that you get wild, big swings in polls before the end of the second convention."

Trump remains highly unpopular on critical questions: Bill Galston, former policy adviser to Bill Clinton and Brookings Institution scholar

Then there's another encouraging sign for Democrats: Clinton looks better once you begin poking into the specific questions asked by pollsters.

"You have to look at the deeper structure of public opinion," Galston says. "You have to look at voters' evaluation of the traits of the different candidates; then you see the raw material for the general election."

Look, for instance, at national security and international affairs, where voters overwhelmingly favor Clinton. She beats Trump two to one on who can be trusted on foreign policy and also by huge margins on caring more about the middle class.

"Every successful presidential candidate has to clear a threshold of being at least acceptable as chief steward of American foreign policy and commander in chief of the armed forces," Galston says. "The more the Clinton campaign can turn the focus of the election toward those areas where she has a decided edge, the better they'll do."

Why the race is looking awfully close

Republicans are lining up behind Trump; this is not going to be a blowout: Richard Benedetto, political scientist and polling expert at American University

Perhaps the worst sign for Clinton is that the new polls blow up the idea that Trump would cause a mass defection among Republican voters.

About 80 percent of Republicans say they'll support Trump over Clinton. That's around as many Democrats are supporting Clinton over Trump at the moment.

"The media decided that Trump is such a buffoon he'd badly blow the race," Benedetto says. "But this race is looking close."

As the Washington Post noted, Trump had no chance if he couldn't convince Republican voters to get behind him. He's certainly cleared that hurdle now.

Are voters increasingly okay with admitting their support for Trump? Michael Ramlet, CEO and co-founder, and Kyle Dropp, executive director of polling and data scientist, both of polling firm Morning Consult

The tightening of the race wasn't a big surprise for the polling firm Morning Consult, which has had Trump within striking distance of Clinton for several months.

"A lot of people are hearing that Trump is more competitive than six or eight weeks ago," Ramlet says. "But we've been telling that story for weeks."

Why is that? Unlike more traditional pollsters, Morning Consult gets its samples through online questions instead of just via in-person and telephone interviews.

Using anonymous online surveys has led Morning Consult to consistently give Trump better numbers than other firms — both now and during the primary — because, according to Ramlet, voters have been embarrassed to tell interviewers they're supporting Trump.

"There was a 6- to 8-point difference between what people would tell an online poll and what they'd tell a live telephone interviewer," he says. "And the effect became more pronounced with higher-income and better-educated respondents."

If that's true, maybe Trump's recently polling rise isn't a result of an ongoing feud in the Democratic primary but instead a growing willingness to reveal to pollsters the extent of what's been his much deeper popularity all along.

Some models have found this should be a Republican year: Julia Clark, senior vice president of Ipsos Public Affairs

If Trump can really just run as a generic Republican with the support of his party's voters, then there's good reason to believe he can beat Clinton.

Clark built a model to look at how some "fundamental" factors going into the presidential cycle — including the president's approval ratings, the state of the economy, and the length of the current party's control of the White House — correlate with which party should be favored in November.

Clark found the Republicans should have a healthy edge in 2016. "If you go on that model alone, there's an 85 percent predictive value it should be a Republican year," she says.

Clark has other polling evidence that helps her think Trump will prove a serious candidate. "Trump's themes are not just the purview of Republican voters; there are independents who buy into a watered-down version of Trump's nativism," she says.

Take the line that "immigrants take jobs away from Americans." When asked, only 41 percent of independents agree with it. By comparison, 56 percent of independents agree with the line, "When jobs are scarce, employers should prioritize hiring people of this country."

"I'm waiting and seeing, because if Trump begins to adjust his rhetoric, these lines might be more universally appealing," Clark says. "I think it's very possible Trump could win the presidency. He certainly has a much better chance than most people are giving him."

The map we see every presidential election is pretty much useless