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Members of the Illinois House and Senate could do a little or a lot.

State legislators return to Springfield on Monday for what will be one of the more peculiar fall veto sessions in the history of the General Assembly.

Because Gov. J.B. Pritzker and the Democratic House and Senate supermajorities see mostly eye to eye, there aren’t many Pritzker legislative vetoes for the House and Senate to consider.

But there is a huge Pritzker proposal he wants the House and Senate to pass as soon as possible, the complicated plans to merge roughly 650 downstate and suburban police and fire pensions into two investment vehicles. At the same time, Chicago Mayor Lori Lightfoot — a fellow Democrat — wants some legislative favors.

Meanwhile, talk of a burgeoning political scandal abounds. One member of the Illinois Senate — Tom Cullerton of Villa Park — has already been indicted in connection with a no-show job with the Teamsters union. Another, Martin Sandoval of Chicago, has been the target of federal search warrants at his home and offices, including at the Illinois Senate.

Will they show up? If so, will they have anything to say about what appears to be multiple corruption investigations into suspected wrongdoing in Chicago, Cook County and the General Assembly in Springfield?

Finally, there are questions surrounding longtime Democratic House Speaker Michael Madigan. Federal search warrants have been aimed at some of his closest political associates, and he’s reportedly on the feds’ radar.

What will Madigan, who’s been keeping a low profile, have to say when he’s exposed to the outside world? Most probably, nothing of substance or nothing at all. He’s a man of few public words.

There is no question, however, that the Legislature is confronting two big issues — the proposed pension consolidation and Lightfoot’s wish list to address her city’s financial problems.

Lightfoot’s proposals are strictly about politics as they relate to policy. Chicago dominates the state, but that doesn’t mean legislators will accede to Lightfoot’s requests.

On the other hand, pension consolidation is about policy as it relates to politics.

Fire and police pension funds are in poor shape, and something has to be done. But can all the interested parties agree on what?

Firefighters support consolidation, while police officers oppose it.

Following the release of a recent report recommending consolidation by a task force he organized, Pritzker made it clear he wants immediate action during the six-day veto session — Monday-Wednesday and Nov. 12-14.

“There have been reports and more reports and more reports. and nothing was done about it,” Pritzker said. “I really believe now is the time.”

The governor’s press office recently reiterated his position while declining to disclose what form the legislation will take.

The General Assembly can’t pass a bill if there’s no bill to pass, and that apparently is what legislators are waiting to see, both party leaders and rank-and-file members.

“... We’re still waiting to review bill language!” said Eleni Demertzis, a spokeswoman for House Republican Leader Jim Durkin.

She described Durkin as “generally supportive of the concept” but in need of more information. Steve Brown, a Madigan spokesman, said pretty much the same thing. Noting that firefighters favor the consolidation plan, while police are opposed, Brown said, “It’s unclear to me what the next steps are.”

A spokesman for Senate President John Cullerton said Democrats will have a caucus meeting Monday to determine how to proceed.

“That’s where things stand,” said John Patterson.

It’s easy to understand the governor’s desire for prompt action. After all, he knows what he wants, and he wants it now.

But that’s a big ask. The consolidation issue is more complicated than what its proponents would have the public believe.

It has an obvious appeal, the theory being that the two funds — one for firefighters and one for police — would have the greater flexibility required to generate higher returns at lower costs.

But there are troublesome details as well, things like transition costs, as well as the financial impact on individual municipal funds.

In other words, it’s complicated.

After all, Pritzker’s task force took months to study the issue while legislators are being asked to rubber-stamp legislation in an atmosphere dominated by rumors about pending corruption probes and Chicago bailouts. It could be an interesting six days.