The EPIC-MRA poll shows Land’s lead has remained fairly constant in polls over the last few months. In the poll's September survey, Peters narrowly led Land by a 38-to-37 percent margin.
Land led Peters by 41 percent to 38 percent in the poll, the latest survey to find a tight race in the Democratic-leaning state and the fourth poll in a row to show her with a slight lead.
Her lead seems partly driven by higher name recognition. Just 55 percent of voters know who Peters is, while 63 percent know who Land is.
Land's campaign crowed about the results.
"Terri Lynn Land is gaining support from Michigan families because they know they can trust her as a mom, small business owner and public servant to fight for them in Washington, D.C.," said Land spokeswoman Heather Swift.
Bernie Porn, president of EPIC-MRA, told the Detroit Free Press that Peters’s negative rating "really hasn’t moved much" despite Americans for Prosperity advertisements targeting his support of ObamaCare.
Peters's campaign took a shot at Land and the AFP ads.
"Former RNC Committeewoman Terri Lynn Land and the Koch Brothers spent more than a million dollars in false attacks trying to distort Gary's record as a proven independent voice for Michigan middle class families and the race is still a dead heat," said Peters spokeswoman Haley Morris. "While Gary is building a strong, grassroots campaign to fight for Michigan middle class families and small businesses, Former RNC Committeewoman Terri Lynn Land shares the same anti-middle class agenda as the Koch Brothers, and it's wrong for Michigan."
Both raised about $1 million in the last quarter of 2013, with Land chipping in $600,000 more from her own pocket.
The live-caller poll of 600 likely voters was conducted Feb. 5-11 and has a margin of error of plus or minus 4 percentage points.
—This post was updated at 10:30 a.m.