A new polls shows a tie between Democratic New York Senator Hillary Clinton and former New York Mayor Rudy Giuliani if a presidential election was held today — and indicates trouble down the political pike for Clinton that her handlers…and her party…will have to anticipate and counter if she is to be elected.

The poll shows Americans have decided turned away from President George Bush, who is now on the way to becoming one of the most unpopular Presidents ever — more unpopular that Richard Nixon. But it also shows reservations against Clinton so ingrained that the Republicans now have more openings than Starbucks Coffee has shops:

Democrats enter the 2008 presidential race with powerful political advantages, but face a tough and unpredictable battle because of the vulnerabilities of front-runner Hillary Clinton.

A new Wall Street Journal-NBC poll shows that Americans have turned sharply away from President Bush and toward domestic issues favoring his partisan adversaries. But offsetting that demand for change in the presidential contest are reservations about Clinton’s truthfulness and ideology, even as Americans applaud her experience and leadership qualities. The result: She’s locked in a dead heat against leading Republican candidate Rudolph Giuliani.

The fact that the Democrats now face a toss-up at a time when Bush and the Republicans otherwise seem on the political ropes on several fronts isn’t good (or reassuring) news for Democrats. Any lead X candidate usually has at the start of a Presidential campaign is greatly tested and can dissipate once the campaign unfolds. If her campaign starts at a dead heat and has an underlying weakness, that weakness could be accentuated during a general campaign.

This means that if Clinton is indeed the candidate, the Democrats (and the Clinton campaign) will have their work cut out for them to overcome Clinton’s negatives…and try to bring up Giuliani’s.

The key question: as the Republicans inevitably try to do the same thing to the former first lady, have her negatives “bottomed out” since so many are rooted in past controversies and perceptions, or is she indeed as her Democratic Party critics suggest the easiest candidate for Republicans to beat? MORE:

By 50% to 35%, the poll shows, Americans prefer that a Democrat gets elected to succeed Bush next November. In a direct matchup of leading candidates, however, that margin shrinks to 46% for Clinton and 45% for Giuliani.

That’s a HUGE impact for a candidate’s negative to have on an election.

The survey, conducted among an unusually large sample of 1,509 adults with an error margin of 2.5 percentage points, shows a remarkable divergence in assessments of Clinton’s personal qualities. While a 51% majority gives her high marks for being “knowledgeable and experienced enough to handle the presidency,” pluralities rate Clinton negatively on honesty, likeability, and sharing their positions on of the issues.

The poll shows Giuliani now the favorite of 33 percent of the Republicans and in the lead. It also shows former Senator and actor Fred Thompson’s campaign fizzling faster than a glass of Alka-Seltzer — going from 23 percent to 15 percent.

Another factor to keep in mind is the independent non-candidacy of New York Mayor Michael Bloomberg.

Some months ago there was a flurry of speculation about him running as an independent but he pooh-poohed the idea. Stories later came out saying he wouldn’t run unless his advisers told him a) there were huge negatives for the top candidates of the two main parties and b) he had a chance of winning, not just being a spoiler or making a political statement.

A Newsweek cover story now says that option is alive again. And when pressed by reporters, the Mayor himself is leaving the door ajar.

If that happens, this would be an election year dominated by three New Yorkers: the Democrat, the Republican and the Independent.

Bottom line: Clinton is closing the sale among Democrats — but is not doing so among the American public. Her ingrained negatives remain.

UPDATE: More bad polling news for Hillary Clinton:

More than eight in 10 Republicans and more than half the married men in a new USA TODAY/Gallup Poll say they definitely wouldn’t vote for Hillary Rodham Clinton for president.

The poll provides an early snapshot of who’s ruling out Clinton, John Edwards and Barack Obama, the three leading candidates for the Democratic nomination.

This “snapshot” in essence is of ugly political storm clouds for Democrats. Republicans will frame their campaign around this support deficit and enlarge it:

Clinton, who tops national polls of Democrats, is strongest within her party. Only 10% of Democrats said they’d rule her out; nearly three times as many said they wouldn’t vote for Edwards.

The new poll found that Clinton would defeat the leading Republican, Rudy Giuliani, in a hypothetical matchup. Still, some Democrats wonder whether she’s potentially unelectable or a drag on candidates lower on the ballot, and rivals such as Edwards say they’re better bets.

This poll and the Wall Street Journal poll show these reservations are not frivolous ones.

In a general election, the poll suggests that Clinton has the least potential for winning votes from Republicans — 84% say they definitely would not vote for her, compared with six in 10 for either Obama or Edwards. Independents show the least resistance to Obama and the most to Edwards.

The poll found that 36% of women wouldn’t vote for Clinton, compared with 50% of men — and 55% of married men. Obama had comparable appeal to women and more to men. Clinton’s appeal overall falls as income rises, the reverse of the findings for Obama.

Pollster Mark Penn, a top Clinton strategist, says Clinton’s strength against GOP hopefuls is growing. “With candidates who are lesser known, typically we see the opposite pattern happen,” he says, citing 2004 nominee John Kerry as an example. Penn also says her appeal to Republican women is rising, and nearly a quarter of them could defect to her in a general election.

Penn may have a point. But it still means Clinton’s party will wage a race carrying a lot of political baggage — and Republicans will do their best to jump on it and pile more on as Democrats and Clinton will try to shed it.