WASHINGTON (AP) — President Barack Obama’s standing in a new Associated Press-GFK poll suggests he could be in jeopardy of losing a re-election bid in November 2012, even as the survey showed that the U.S. public’s outlook on the economy appears to be improving.

Obama’s re-election prospects are essentially a 50-50 proposition, according to the poll. It found that most Americans say the president deserves to be voted out of office even though they have concerns about the Republican alternatives.

The Republican candidates held their last debate Thursday before the Jan. 3 Iowa caucuses lead off the battle for the nomination to challenge Obama. Former House speaker Newt Gingrich looks to maintain his recent lead while former Massachusetts governor Mitt Romney and other rivals work to tear him down.

The poll found Americans were evenly divided over whether they expect Obama to be re-elected next year.

For the first time, the poll found that a majority of adults, 52 percent, said Obama should be voted out of office while 43 percent said he deserves another term. The numbers mark a reversal since last May, when 53 percent said Obama should be re-elected while 43 percent said he didn’t deserve four more years.

Obama’s overall job approval stands at a new low, with 44 percent approving and 54 percent disapproving.

Heading into his re-election campaign, the president faces a conflicted public. It does not support his steering of the economy, the most dominant issue for Americans, or his overhaul of health care, one of his signature accomplishments, but it also is grappling with whether to replace him with Romney or Gingrich.

Romney was still campaigning in Iowa on Friday as he looked to halt Gingrich’s momentum. He planned a campaign swing later in the day through South Carolina, whose governor, Nikki Haley, endorsed him Friday morning, saying Romney is “someone that knows what it’s like to make a decision and lead.” She announced her endorsement Friday on Fox News.

Gingrich was returning to Washington after comparing himself to Ronald Reagan in Thursday’s debate and insisting that he can defeat Obama in 2012. He added that it was laughable for his rivals to challenge his conservative credentials.

Despite the soft level of support, many are uncertain whether a Republican president would be a better choice. Asked whom they would support next November, 47 percent of adults favored Obama and 46 percent Romney, the former Massachusetts governor.

Against Gingrich, the Republican front runner and former speaker of the House of Representatives, the president holds a solid advantage, receiving 51 percent compared with 42 percent.

The Associated Press-GfK Poll was conducted Dec. 8-12 by GfK Roper Public Affairs and Corporate Communications. It involved landline and cellphone interviews with 1,000 adults nationwide and has a margin of sampling error of plus or minus 4 percentage points.

The wild card in the Republican race is Texas Rep. Ron Paul, with the small-government libertarian surpassing Romney in some polls of Iowa voters.

In Thursday’s debate, Paul said the U.S. has no legitimate claim to block Tehran from developing a nuclear weapon and he expressed his anti-war, anti-interventionist views so vehemently that he may have turned off mainstream Republicans who otherwise might have helped him to a surprising first-place finish.

“To declare war on 1.2 billion Muslims and say all Muslims are the same, this is dangerous talk,” Paul said of the idea of taking pre-emptive action to prevent Iran from developing nuclear weapons. “Yeah, there are some radicals. But they don’t come here to kill us because we’re free and prosperous … They want to do us harm because we’re bombing them.”

Fellow candidate and Rep. Michele Bachmann said, “I have never heard a more dangerous answer for American security.”

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Associated Press writers Ken Thomas and Jennifer Agiesta contributed to this report.

Copyright 2011 The Associated Press.