The City Council is making “glacial progress” toward shedding its reputation as a rubber stamp because Mayor Rahm Emanuel is “undeniably weaker” and the city’s recalcitrant problems are requiring more painful solutions, a new study shows.

There’s almost nothing that angers Emanuel more than being reminded that he’s been “weakened politically” by being forced into Chicago’s first mayoral runoff and by his handling of the Laquan McDonald shooting video shortly after being re-elected.

But that’s the unmistakable conclusion of the new study released Wednesday by the political science department of the University of Illinois at Chicago.

It shows that there have been 67 divided roll call votes — roughly three per month — in the two years since the new City Council was sworn in. That’s twice as many as there were during Emanuel’s first term.

In addition, the level of opposition in those divided roll calls has increased.

Only five aldermen voted with the mayor 100 percent of the time, with 22 more sticking with Emanuel 90 percent of the time. That’s four votes short of the number needed to pass legislation.

A year ago, 28 aldermen were 90 percent supporters of the mayor.

During Emanuel’s first term, 37 aldermen — three-fourths of the 50-member City Council — supported the mayor at least 90 percent of the time.

Former independent Ald. Dick Simpson (44th) is a principal author of the study.

He contributed $5,000 to Chicago Teachers Union President Karen Lewis before a brain cancer diagnosis forced her to drop out of the mayoral race. Simpson then contributed $10,250 to Lewis’ hand-picked replacement, vanquished mayoral challenger Jesus “Chuy” Garcia.

Simpson also has been a reliable contributor to the City Council’s anti-Emanuel Progressive Caucus and to its individual members, who are among the mayor’s most outspoken critics.

But Simpson argued Wednesday that the “numbers don’t lie,” in spite of his political history.

Although Emanuel has yet to lose a vote or exercise his veto power, the mayor is “undeniably weaker” than he was during his first term, Simpson said.

And because he is less popular and solutions to Chicago’s intransigent problems — like school funding, the $30 billion pension crisis and police misconduct — have become more painful and costly, aldermen are less afraid to oppose him, he said.

“The level of dissent in the City Council is growing and more aldermen are engaged in the tussle to shape city legislation,” Simpson told a City Hall news conference.

“Clearly, the City Council is less of a predictable rubber stamp than it was during Mayor Richard M. Daley’s 22-year reign or Rahm Emanuel’s first term in office,” he said. “Nonetheless, the movement from an absolute rubber stamp is still slow and, you might say, glacial in its improvement.”

And what exactly does this bode for Emanuel’s chances of winning re-election, if he chooses to seek a third term?

Simpson, an admittedly biased observer, said it depends who steps up to challenge Emanuel, a prolific fundraiser who spent $24 million to beat the relatively unknown and late-starting Garcia.

“If you had a viable candidate running against him with more money than Chuy Garcia had last time … closer to $10 million … Rahm Emanuel, at the moment, would be in trouble,” Simpson said.

“Rahm Emanuel’s popularity is improving and he still has roughly two years in which to regain the confidence of Chicago,” he said. “But if the election were held today, I think Rahm Emanuel could well lose if there were a proper opponent on the other side.”

Mayoral spokesman Matt McGrath offered a pithy response to Simpson’s annual blast.

“The sky is blue, water is wet, and Dick Simpson still doesn’t like the Mayor. You don’t need a report to know that,” McGrath wrote in an email.

Aldermen from all sides also were not surprised by Simpson’s findings.

They’ve been living it — and the Chicago Sun-Times has been reporting on it — ever since Emanuel survived the runoff and rolled right into the resignation of his now-convicted Schools CEO Barbara Byrd-Bennett and the Laquan McDonald controversy.

“It’s a combination of all of those things. He has taken a hit after Laquan McDonald. The decisions are becoming more difficult as we don’t have the money from the state and/or our own tax revenue or anything else to sell. And people who have come into the City Council with a different philosophy that it’s going to be divided no matter what,” said Education Committee Chairman Howard Brookins (21st), former chairman of the Black Caucus.

Brookins noted that some of the divided roll calls “don’t mean anything,” either because the issue is innocuous or because they know full well that Emanuel already has the votes.

That gives aldermen the freedom to do some political posturing, he said.

“Because of that, aldermen are now inclined on the self-preservation front, to say, `I’ll just vote no on this. It’s gonna pass anyway. Why not just do it so my opponent doesn’t pick up Dick Simpson’s report and say, `He voted 100 percent with the mayor. So something must be wrong with you.’ ”

Ald. Walter Burnett (27th) noted that aldermen have walked the tax plank three times to solve the pension crisis with no end in sight. They’re bracing for another round of difficult votes to save the Chicago Public Schools.

“When people get closer to election time, especially guys who aren’t as solid in their community, those guys do what’s popular,” said Burnett, one of Emanuel’s staunchest Council supporters. “The guys who are solid in their communities — they do what’s right.”