The pollster blamed the preference for Democrats on Republicans' "extremism" and "obsession" with repealing the healthcare law. The House GOP has held 40 votes to repeal, defund or dismantle the reform since its passage.
"Debate over ObamaCare will play to the Democrats' advantage in 2014," said Geoff Garin, president of Hart Research Associates.
"There is a very strong message here that making the case against repeal and for fixing and improving ObamaCare is a very strong political position."
The survey presents a path forward for Democrats nervous about a botched ObamaCare rollout ruining their chances to control the House and Senate in 2015.
More than 20 House Dems recently sided with the GOP against the White House on votes to delay the law's employer and individual mandates.
The moves were interpreted by some as positioning ahead of 2014, when the GOP hopes to pick up a swath of seats by hammering less popular aspects of ObamaCare.
According to Garin, candidates on the left should emphasize their willingness to amend or adjust elements of the Affordable Care Act if they want to appeal to undecided voters.
"This idea of totally repealing [the law] is a distinctly minority position in today's electorate," he said.
The survey recorded 36 percent who support ObamaCare's repeal, while 40 percent want to leave the law as is or make minor changes. Another 18 percent hoped for major changes.
Those results somewhat mirror a recent poll by CBS News that found a record 39 percent who want to repeal the healthcare law. Another 36 percent said it should be left alone or expanded.
Wednesday's survey was comprised of interviews with 205 likely 2014 voters from July 12-17.