A new poll released Wednesday indicates President Barack Obama is holding onto his lead over Mitt Romney in Wisconsin, a crucial battleground state this November.

According to the Marquette University Law School survey, Obama is ahead of his Republican challenger by eight percentage points, 51% to 43%.

The president had the same margin over Romney when the poll was conducted in late May. It's worth noting that the margin narrowed slightly in June to a six point difference in favor of Obama--49% to 43%--but is now back to eight points.

CNN's Electoral Map rates Wisconsin, a state that holds 10 electoral votes in the general election, as leaning towards Obama.

However, Republicans have indicated they consider the Badger State up for grabs this November, especially after Republican Gov. Scott Walker survived a contentious recall effort in June.

"You know what, we're going to win Wisconsin," Romney told a crowd at a campaign stop on his five-day, six-state bus tour last month.

"I'll tell ya, I think President Obama had just put this in his column," he added. "[Obama] just assumed at the very beginning Wisconsin was going to be his."

As expected, the health of the economy proves to be an influential factor among Wisconsin voters, the poll shows. The 22% of voters who think the economy has improved tend to support Obama, while the 33% who believe it has gotten worse are more supportive of Romney.

Regarding Walker, who's also a Romney surrogate and rumored to be a potential running mate pick, the poll shows the Republican governor with a 50% job approval rating, compared to 44% of those who disapprove. Also significant, a majority--52%--of independents approve of Walker's handling of his job, while 41% disapprove.

In addition, the state is undergoing a big Senate race this year, with Republicans still competing in a crowded primary set for August 14. Former Gov. Tommy Thompson leads the GOP field with the backing of 35% of likely primary voters.

The Republican winner will face off against Democratic Rep. Tammy Baldwin this fall. According to a hypothetical matchup in the poll, Thompson has a small advantage over Baldwin, 45% to 41%.

Marquette interviewed 1,000 registered Wisconsin voters by phone July 5-8, with a sampling error of plus or minus 3.2 percentage points.

-- CNN's Rachel Streitfeld and Paul Steinhauser contributed to this report.