With just seven weeks to go before Iowa holds the first nominating contest of the GOP presidential primary, voters in the state remain ambivalent about their choices. According to a new Bloomberg News poll, businessman Herman Cain leads the pack with 20% support among registered Republican leaning voters, followed by Ron Paul at 19%, Mitt Romney at 18% and Newt Gingrich at 17%. The poll, which was taken Nov. 10-12, has a margin of error of 4.4 percentage points, meaning the four candidates are in a statistical dead heat.

Sixty percent of respondents said they could be persuaded to support another candidate as their first choice, another sign that the field is nowhere near settled.

While social issues have traditionally been very important in the Iowa caucuses, the poll suggests Iowans this year are far more focused on the economy. Seventy-one percent said fiscal issues are most important to them.

Just 25% said gay marriage was a “critical” issue in evaluating the candidates; 38% said it is “not important.” Similarly, 33% said abortion was a critical issue but 24% said it is not important. Seventy-seven percent said government spending and reducing debt was a critical issue, compared to just 1% who said it was not important.

The poll was conducted by Selzer & Company, the Des Moines firm that was alone in correctly predicting Barack Obama’s upset victory in the state’s Democratic caucuses in 2008.

Today’s poll spells good and bad news for each of the Republican candidates who are vying to take on Obama in 2012:

Herman Cain’s support in Iowa dropped about three percentage points since a Des Moines Register poll taken Oct. 23-26, also by Selzer & Company, found him at 23%. The Bloomberg News poll was taken as four women alleged that Cain had sexually harassed them in the 1990s, but it is unclear how much the allegations may have hurt his standing with voters.

Twenty-nine percent said they believe Cain when he says he never sexually harassed anyone and 37% said they are waiting to make up their minds. Just 14% said they don’t believe him. More than two-thirds – 69% -- said they would not rule out a candidate who has been accused of sexual harassment.

Also good news for Cain: 45% of respondents said they would “definitely” support him in a general election against President Obama.

Texas Rep. Ron Paul has the most solid base of support. Of likely caucus-goers who say they’re decided on who they will back, 32% have chosen Paul, according to a Bloomberg analysis of the poll results.

Paul’s campaign has also made the most contact with voters – 67% said they had been contacted by the Paul campaign, followed by 61% who report being contacted by Minnesota Rep. Michele Bachmann and 47% contacted by Texas Gov. Rick Perry.

Like Cain, former Massachusetts Gov. Mitt Romney has also seen his support slide since the last Iowa poll, which had him at 22%. He’s now at 18%, his lowest level of support in Iowa this year.

Even worse, 58% say they would rule out a candidate who has favored a mandate to buy health insurance. And just 7% list Romney as the candidate who would do the most to halt illegal immigration.

The good news for Romney is that he appears to be picking up new supporters – just 41% of those who back him said they also went for him in 2008, according to the Bloomberg analysis. Romney lost the Iowa caucuses in 2008 to former Arkansas Gov. Mike Huckabee, despite spending about $10 million in the state.

Matched up with Obama, 45% said they would definitely support Romney and just 18% said they would probably not.

Newt Gingrich has enjoyed a recent boost in the polls after a sluggish summer that began with the embarrassing departure of more than a dozen key campaign staffers.

But the Bloomberg poll suggests Gingrich’s marital history – he is on his third marriage and has admitted to having an extramarital affair – may mean trouble for the former House speaker. Respondents were split – 48% to 49% -- over whether they would rule out a candidate who has been married three times and had extramarital affairs.

Rick Perry’s disastrous debate performance last week seems not to have impacted his already low support in Iowa.

As was the case in late October, Perry has just 7% support.

He seems to score highest with voters on immigration – 16% say he is the candidate who would do the most to end illegal immigration. But his tax proposal to allow people to pay a 20% flat rate has just 14% support, compared to 32% who favor Romney’s proposal to make the Bush tax cuts permanent, then work toward overhaul of the system.

Michele Bachmann’s aggressive campaign strategy in Iowa has failed to pay off as she continues to lose support there. Bachmann enjoyed 22% support in June, then won the Ames Straw Poll. But by late-October, her support had fallen to 8%. She’s now at 5%.

Former Pennsylvania Sen. Rick Santorum, at 3%, claims to have visited all 99 Iowa counties.

The one bit of good news for former ambassador Jon Huntsman – and for Romney -- is that 91% said they would not rule out a candidate because he is a Mormon. Huntsman, at 1%, is not aggressively competing in Iowa.