President Obama has lost his luster among voters in swing state Ohio since 2008, but he remains in a steady tie with GOP front-runner Mitt Romney in a hypothetical 2012 race, according to the latest Quinnipiac University poll.

Ohioans said they'd prefer Obama over Romney, 45 to 41 percent, if the election were held today, a statistical dead heat given the poll's margin of error of 4.2 percentage points.

The two have been deadlocked for the lead in each of five Quinnipiac polls in Ohio since July, with Obama staying closely in the race despite majorities of voters disapproving of his job performance and saying he does not deserve a second term.

Forty-eight percent of Ohio voters have a favorable impression of Obama, compared with 47 percent who do not, according to the poll.  Ohioans are equally divided over Romney, with 36 to 34 percent holding favorable-unfavorable views.

"With Ohio being perhaps the most important single state in the country when it comes to the Electoral College math, all indications are that if Romney is the Republican nominee, it will be a very, very close contest," said Peter Brown of the Quinnipiac University Polling Institute in Hamden, Conn.

Obama won Ohio by 5 percentage points over John McCain in 2008, carrying 52 percent of the vote, but his support has waned with the economy still struggling to recover.  The unemployment rate in Ohio stood at 8.5 percent in December, the same as the national average.

Only 44 percent of Ohioans said they approved of Obama in the Quinnipiac poll, conducted Jan. 9-16. Among all-important independents, a majority - 53 percent - said they disapproved.

No candidate for president since 1960 has won a general election without carrying Ohio.

"The president's problem is getting back the voters who voted for him in 2008 but went for [Republican] John Kasich for governor in 2010," Brown said. "His main obstacle may be that voters say 48 to 42 percent that Romney is better able to fix the economy."

Republicans say the numbers ought to be a "huge warning sign" for Obama in Ohio, which he has visited 16 times in the past three years.

"Obama has literally been campaigning in Ohio since he became president, and his numbers still linger where they are after all that," Republican National Committee spokeswoman Kirsten Kukowski noted. "Republican candidates haven't even begun seriously campaigning there."

In anticipation of the fights to come, the Obama campaign is preparing to substantially expand its presence and profile in the Buckeye State with plans to open "several dozen" new field offices in the next few months, a campaign official said.  The president's operation already has three outposts in Ohio with a headquarters in Columbus.

Obama aides have credited successful Democratic grassroots organizing campaigns late last year with adding "thousands and thousands" of new voters to registration rolls. Volunteers have knocked on more than 100,000 doors and held at least 3,000 face-to-face conversations with prospective voters since April, an  Obama campaign official said.