ANN ARBOR, Mich. — Michigan coach Rich Rodriguez was handed a blue button with “Beat Ohio State” in maize letters when he was introduced as the new leader of college football’s winningest program.

Rodriguez said earlier this week he has kept the button on his desk.

After being asked about the button later by a visitor to his office, Rodriguez had to do some searching. He found it tucked under some paper in the top drawer of the desk.

“I put it in there one day when I got mad,” Rodriguez said.

It would be tough to figure out what day that was because there’s been a lot of reasons for him to be angry during his two tumultuous seasons in Ann Arbor.

The Wolverines started 4-0 this season, earning a spot on the cover of Sports Illustrated, and Rodriguez was hailed for the turnaround after losing a school-record nine games last year.

Two closely contested losses on the road to Michigan State and Iowa snowballed into a skid that has included only one win — against Delaware State — in a seven-game stretch.

The collapse has made Saturday’s game at home against No. 9 Ohio State more important than usual, but in an unusual way for Michigan.

If Michigan beats its rival for the first time since 2003, it will salvage some pride with a bowl bid and get much-needed practices.

If not, the Wolverines will have a losing record in consecutive years for the first time since the 1962-63 seasons and will endure another miserable offseason that might be compounded if the NCAA delivers bad news during an investigation it plans to complete by the end of the year.

Rodriguez hasn’t gotten to enjoy many days since a messy divorce with West Virginia led to a turbulent transition at Michigan.

He insisted, though, he doesn’t regret leaving West Virginia or turning down an opportunity to be Alabama’s coach.

“It’s taxing on my family and me, but this is a big-boy business,” Rodriguez said in an interview with the AP. “I’ve been at big schools before. We had drama, but not as much as here.

“It’s a wonderful profession, but when things are not going the way you’d like, it certainly takes a toll.”

Rodriguez took his latest hit off the field on Monday, when an internal audit was released in untimely fashion with details about the football program failing to file forms that track how much players workout and practice. The forms are used to comply with NCAA rules.

He said Wednesday the process of filing forms was corrected as soon as he learned it wasn’t happening. He declined further comment because of an ongoing NCAA investigation.

The office of university audits sent Rodriguez a memo on July 24, stating that forms from the 2008 regular season had not been submitted.

The Detroit Free Press, citing anonymous players, reported a month later that Michigan exceeded NCAA limits regarding practices and workouts.

Detroit Lions offensive lineman Jon Jansen, who helped the Wolverines win the 1997 national championship, says it’s disappointing to know people with ties to the school have conspired against Rodriguez since he replaced the retiring Lloyd Carr in part because they wanted somebody else — such as LSU’s Les Miles — hired.

“You’d have to be blind to not see there are divisions among Michigan folk,” Jansen said. “I think that while he’s there, he should get as much support as he can get.

“Whether you are for or against Rich Rod, everybody should be for Michigan. I hope he’s successful because I want Michigan to be successful.”

An e-mail was sent to every member of the school’s board or regents, asking for comment on Rodriguez and the program, and no one responded.

University of Michigan president Mary Sue Coleman declined an interview request, but issued a statement.

“As I’ve said before, I continue to support our coach and our football program,” Coleman said in a statement sent by her office.

If Michigan did want to fire Rodriguez — who signed a six-year deal worth $2.5 million per season — it would likely be an ugly process.

According to his contract, Rodriguez can be fired for cause if the NCAA, the Big Ten or the school determines he has committed a major violation of NCAA rules or he has intentionally committed any other type of violation of NCAA rules.

If the school completes a four-step process to fire Rodriguez for cause, it “shall be without liability to Rodriguez,” according to the contract he signed Oct. 24, 2008.

Athletic director Bill Martin, who hired Rodriguez and is retiring by September at the latest, tried to voice as much support as he could as his outgoing boss.

“We’re in a transition and we all have to be prepared to stay the course,” Martin said earlier this week. “Is our record a surprise? Sure. Do I totally support Rich? Absolutely. You don’t want to make excuses, but take a look at our personnel. We have only 71 players who came here on scholarship. We’ve got freshman going against fifth-year seniors in a lot of places.

“We didn’t have a lot of candidates to replace Lloyd’s best players in his last season.”