Washington (CNN) Democrats knew a general election battle between Hillary Clinton and Donald Trump would be rough, but many never considered the potential of a nailbiter.

During a primary in which Trump usurped the GOP establishment, alienated crucial sectors of the general electorate on issues like immigration and abortion and dinged his own approval ratings, many Democrats salivated at talk of a November duel with the billionaire.

Now, as Trump prepares for a general election showdown and a pair of new polls show a statistical dead heat, veteran Democrats warn there is little room for complacency.

"It will be close," said Mark Alderman, a veteran Democratic Party fundraiser who worked on President Barack Obama's transition team.

"I think that Trump as the nominee is an advantage for our party, but not nearly the advantage that some people had thought and hoped it would be," said Alderman, now with Cozen O'Connor Public Strategies. "I think he has proven to be a far more formidable candidate than expected."

Jay Carson, Clinton's 2008 press secretary who has also worked for her family's foundation, recently took to Instagram to sound the alarm on Trump

"Here's the bad news -- this guy can win the general election pretty damn easily," Carson, who is now a producer on the Netflix series "House of Cards" and a Principal at Bloomberg Associates, wrote on his private account. "I hear far too many of my liberal friends calling him a 'joke' and acting like the general (election) is in the bag which is nuts because he's dangerous and he has a path to victory."

Trump became the presumptive Republican nominee earlier this month following the Indiana primary, ending any talk of a contested convention and allowing him to enjoy the luxury of setting his sights exclusively on November. Clinton, meanwhile, is the likely Democratic nominee but still fighting Bernie Sanders, who has spoken of taking their race to the national convention in July. That's hurt her ability to completely turn to the battle with Trump.

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Early polls paint a mixed picture. A CNN/ORC poll from the beginning of May found Clinton leading Trump by 13 points. But there is increasing evidence of a 'Trump bump' in polling as the billionaire consolidates Republican support.

A Fox News poll this week actually showed Trump leading Clinton 45% to 42%, findings that were within the survey's margin of error. Meanwhile, a New York Times/CBS News national survey released Thursday has Clinton up by six points.

A new Washington Post/ABC News poll released Sunday finds a statistical dead heat, with Trump leading Clinton 46% to 44% among registered voters, figures that represent an 11% swing since March. The former secretary of state leads by six points among all adults -- down from an 18% lead in March.

And a new NBC News/Wall Street Journal poll , also released Sunday, shows a similar pattern: Clinton 46% to Trump's 43% among registered voters -- a previous survey had her up 50%-39%.

Quinnipiac University polls in swing states Ohio, Florida and Pennsylvania last week had the rivals effectively neck-and-neck.

Polls this far ahead of a general election cannot accurately predict the political environment in November. But they do suggest a competitive race and reflect a nation that is politically split down the middle.

Re-doing the electoral map

Making things more difficult is the fact the 2016 election continues to rewrite the conventions of politics and includes several variables that could have an unpredictable impact on public sentiment.

The biggest factor weighing against a close election is the electoral map -- which Democrats are gathering around them like a security blanket as it suggests their nominee will have the edge. It took only a five percentage point edge in the popular vote in 2012 for Obama to easily defeat Mitt Romney, 332 electoral votes to 206.

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This time around, most analysts agree there are more electoral votes that appear safe for Democrats than are in Republican hands -- meaning Trump will have to perform far more strongly in swing states than GOP candidates did against Obama.

For instance, the latest electoral map compiled by the University of Virginia Center for Politics assumes 190 electoral votes are safe for Democrats and 142 are assured for Republicans. Once 57 likely Democratic votes are added, Clinton theoretically comes within 23 electoral votes -- or a win in Florida, or in a trio of swing states Virginia, Colorado and Nevada -- of claiming the presidency. Trump has a much thinner margin for error.

Still, there are some reasons why 2016 could be much closer than 2012. For one, Clinton is trying to pull off the historically tough assignment of winning a third consecutive White House term for her party. Then, it is far from certain that she will be able to reassemble the coalition of minority, young and educated white voters that backed Obama — or that the President's supporters will prove as enthusiastic about Clinton.

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Then there is the theory that Trump could drive up Republican turnout. Trump has repeatedly claimed he will bring in Democrats and disaffected GOP voters who have felt alienated by the failures of the U.S. political system.

"The Republican Party has become more dynamic, it's become more diverse. We're taking from the Democrats, we are taking from the independents. We have a lot more people," Trump said in March in his Super Tuesday victory speech. "I have millions and millions of people."

Trump's opposition to free trade message is tailor-made for the Rust Belt swing states that currently lean towards the Democrats, like Wisconsin, Michigan, Ohio and Pennsylvania. Still, he may have to watch his flank. Recent polling in solidly Republican states like Georgia and Arizona suggest Clinton may be competitive, partly due to her popularity among minority voters, pointing to a possible insurance policy against losses in the Midwest.

The most unpopular candidates ever

When Trump and Clinton face off, they will become the most unpopular nominees of two major parties in many years, making the task they both face in shifting undecided voters their way more difficult than ever.

In the CBS/New York Times poll, Trump had a favorable rating of 26% and an unfavorable mark of 55%. Clinton was viewed favorably by 31% of voters and unfavorably by 52%.

Such antipathy in the electorate, makes it a tough call for analysts to model turnout in November.

If Clinton does get a 2012-style turnout, she will likely win. But Trump could make things close if he is able to reshape the Republican coalition.

"There is no guarantee that traditional survey research is going to be adequate to the Trump phenomena," said William Galston, a Brookings Institution senior fellow who worked in the Bill Clinton White House.

"People have four choices in this election. You can vote for one or the other, you can cast a protest vote or you can simply stay home," Galston said. "And the election may well be decided by the comparative weight of the abstentions."

Clinton needs to maximize turnout from Latino, African-American, women and young educated voters, and hopes to peel away some Republicans who believe Trump has isolationist instincts that represent a dangerous departure on foreign policy.

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Clinton is already making a case that the billionaire is not qualified to be president, lacks the knowledge, temperament and experience to serve as commander-in-chief and would alienate U.S. allies and make the world more dangerous while dividing the nation along gender and ethnic lines.

"I know how hard this job is, and I know that we need steadiness as well as strength and smarts in it, and I have concluded he is not qualified to be president of the United States," Clinton said in a CNN interview on Thursday.

Trump, meanwhile, is betting on Clinton fatigue, billing the former secretary of state and her husband, former President Bill Clinton, as "crooked" and scandal-tainted and as the heir to an administration he says has left America weak. He also complains the U.S. has become a hostage to political correctness in dealing with threats from the Muslim world, and is being ripped off by trade deals that benefits rivals like China.

Clinton may also be vulnerable on the economy.

Quinnipiac polls showing Trump had double digit leads in the three swing states over Clinton on who would best handle the economy hardly calmed their nerves and pointed to an alarming vulnerability for Clinton in areas of the electoral battleground that could add up to a tightly contested election.

"Blue-collar white independents give Donald Trump some credit on the economy because of his message and his business background," said Democratic pollster Celinda Lake, who conducts the George Washington University Battleground poll, calling for the kind of intense advertising campaign against Trump that helped Democrats eviscerate the character and business record of former Bain Capital venture capitalist Romney in 2012.

"I think to ensure victory, we need to take that away from him. We need the Bain project -- that says who got hurt by his economic policies," Lake said. "We need an aggressive economic message and our party has not had one."