(CNN) - Republican Gov. John Kasich of Ohio has an advantage over a Democratic challenger in next year's gubernatorial election, but that margin is narrowing and less than half of voters believe Kasich deserves re-election, according to a new poll.
A Quinnipiac University survey released Tuesday shows the incumbent governor has a 44%-37% lead over Democratic candidate and Cuyahoga County Executive Ed FitzGerald.
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Kasich's lead over FitzGerald however, was twice as big in a June 25 survey by Quinnipiac, before FitzGerald announced his bid for governor.
While the Democrat has gained ground in the polls, he still has a long way to go in terms of name recognition; 71% of voters don't know enough about him to say whether they have a favorable or unfavorable opinion of him.
"It will take a lot of money and time for the Cuyahoga County Executive to reach those voters, but introducing himself to them is his job one," Peter A. Brown, assistant director of the Quinnipiac University Polling Institute, said in a release. "While FitzGerald is trying to define himself, Kasich can be expected to spend a pretty penny trying to negatively define the Democrat."
For Kasich, who some consider a potential presidential contender, his approval ratings have drastically increased since he took office in 2011 and received sharp criticism for signing into law restrictions on collective bargaining rights.
A majority of voters–52%–now approve of the job Kasich is doing as Governor.
"His approval ratings mark a huge turnaround from his first two years, when his job approval was in the 30s and Democrats were licking their chops at the prospect of making him a one-termer," Brown said. "But he's below the 50 percent mark in the matchup and on whether he deserves reelection."
Forty-eight percent of Ohio voters say he should serve another term, while 39% say he doesn't deserve another four years in office.
The GOP Governor made headlines with his decision to accept federal subsidies to expand the number of people eligible for Medicaid, a major piece of the Affordable Care Act that governors can opt out of. About half of states have accepted the expansion. Many Republican governors have rejected it.
In Ohio, 51% of voters support expanding Medicaid, while 40% say it's a bad idea, according to the poll. Nearly a quarter of registered voters–23%–say they are less likely to vote for Kasich because of his decision, while 19% say it makes them more likely to vote for him. But more than half–54%–say it won't affect their vote.
"Because of Kasich's Medicaid expansion, 24 percent of Republicans say they are less likely to vote for him. History tells us, however, that many of those alienated party members come home on Election Day because they find the other candidates less palatable," Brown said.
Quinnipiac University surveyed 1,361 registered voters by telephone from November 19 – 24, with an overall sampling error of plus or minus 2.7 percentage points.