Former Massachusetts Gov. Mitt Romney leads President Obama in Michigan, according to a new poll.

Romney, whose father was governor of the Wolverine State, leads Obama in a head-to-head matchup by 46 percent to 42 percent, within the survey's four-point margin of error.

Michigan is likely a must-win for Obama. He took 57 percent of the vote there in the 2008 presidential race after Sen. John McCain (R-Ariz.) gave up on the state and pulled out resources a month before the election. But a brutal local economy has hurt Obama with Independents: in the poll, he trails Romney 42 percent to 31 percent with that key group.

Another worrying trend for the president: Detroit, the anchor of any Democratic coalition in the state, has continued to hemorrhage people, losing a quarter of its population since 2000. The state's African-American population has also dropped significantly.

The poll of 600 likely voters was conducted from July 9 to July 11 by the Lansing-based EPIC/MRA.