Dem poll: GOP Rep. Benishek in tough spot in Michigan

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Benishek also has 79 percent name recognition from voters, while McDowell is at 48 percent despite having run against Benishek in 2010, a sign that the pro-gun, anti-abortion-rights Democrat may have more room to grow. The Hill rates the race a "toss-up."

The poll of 402 likely voters was conducted by Democratic pollster Garin-Hart-Yang from June 19-20, and has a margin of error of 4.9 percentage points.