President Obama scheduled a trip to a Chrysler plant here to boast of the car maker’s turnaround following the billions it received in 2009 as part of a broader “bailout” of the American auto industry.

But in a critical state for his 2012 reelection prospects, Obama was forced to balance the positive news of Chrysler with other signs that the American economy is struggling under his stewardship. A few hours before he arrived Friday, the Labor Department announced that the unemployment rate had increased to 9.1 percent, the second straight month it has gone up.

And the resurgence of both Chrysler and General Motors, both recipients of loans from Obama’s administration in 2009, comes amid troubling economic signals: declines in manufacturing and car sales and a large divide between the political parties on increasing the federal debt ceiling.

“I placed my bet on you. I put my faith in the American worker. And I’ll tell you what -- I’m going to do that every day of the week, because what you’ve done vindicates my faith,” Obama told a group of more than 200 workers on the factory floor of a plant where Jeep Wranglers are made.

He added, “Today, all three American automakers are turning a profit. That hasn’t happened since 2004. Today, all three American automakers are gaining market share.”

But while he did not specifically refer to the new unemployment data, he addressed concerns about the broader American economy .

“I don’t want to pretend like everything is solved. We’ve still got a long way to go not just in this industry, but in our economy; for all our friends, all our neighbors who are still feeling the sting of recession,” he said, listing the earthquake in the Japan, unrest in the Middle East and high gas prices as factors contributing to the sluggish economy. “There’s nobody here who doesn’t know someone who is looking for work and hasn’t found something yet.”

Obama tried to focus attention on Chrysler, which has now paid back most of the $12.5 billion it borrowed from the government in 2008 and 2009. The Treasury Department announced Thursday it has reached an agreement to fully withdraw from its ownership stake and other investments in Chrysler, which is effectively operated now by the Italian car maker Fiat.

“We would not be here today without his commitment,” said Jill Opial, a production operator at the plant who introduced Obama.

The Obama administration and congressional Democrats are aggressively touting the recent successes of Chrysler and General Motors, arguing the president’s decision two years ago to invest billions in the two companies shows he has the right ideas for the economy, even as unemployment has remained at high levels throughout his presidency. The White House released a 10-page memo titled “The Resurgence of the American Automotive Industry” this week highlighting Chrysler and GM’s turns from government-sponsored bankruptcy to profitability.

As first reported in the Toledo Blade, Obama campaign officials have been filming and meeting with a production assembly worker at the plant here for possible inclusion in a campaign commercial.

The auto bailout fits in a broader narrative the White House is trying to establish for Obama’s reelection campaign, namely that the president has taken on tough problems that previous presidents did not resolve, such as health-care reform. The Obama campaign wants to cast the president as a strong leader, particularly to independent voters who may not agree with every policy decision he has made.

The auto bailout serves another purpose as well: illustrating how the president saved jobs in swing states such as Michigan and Ohio that he will need to carry in next year’s elections.

And on this issue, Democrats think the Republicans running against Obama are vulnerable, particularly former Massachusetts governor Mitt Romney, who in 2009 attacked Obama’s plan to help these auto companies.

But as the jobs numbers released Friday showed that campaigning on an economic recovery is complicated for Obama. The jobless rate remains high, and unemployment among blacks, a key electoral block for the president, is now more than 16 percent. In announcing his candidacy this week, Romney said, “The economy is in crisis today.”

Obama, while casting the economy as improving, did not ignore the problems.

“We’re going to pass through some rough terrain that even a Wrangler would have a hard time with,” he said.