Quinn did not endorse Cohen in the primary and has called on his running mate to step aside if he cannot resolve the controversy.
"The governor has called on Mr. Cohen to do what's best not only for the ticket, not only for the Democratic Party but for the state of Illinois," said Elizabeth Austin, communications director for Quinn's gubernatorial campaign. "We are on the brink of financial disaster of unprecedented proportions. It is critically important that the elected leaders on both sides of the aisle work together with a sense of urgency to preserve education, health care assistance to seniors, to people with disabilities."
Quinn faces a tough re-election himself for the seat he occupied after Gov. Rod Blagojevich was ousted.
"I think voters have really begun to focus in on the Democratic side and ask themselves, is it really enough not just to be Rod Blagojevich," Chicago Tribune's veteran political reporter Rick Pearson said on "Top Line" Monday.
Rothenberg's Gonzales said the Cohen saga is unlikely to impact Quinn but the governor has to walk a fine line until the election.
"I think Quinn was already in a competitive race on his own," he said. "He can't afford to make mistakes and the party in general can't afford to make mistakes. If we are still talking about Cohen in October, Democrats are going to have a real problem."
Quinn's campaign said it expects the issue to be resolved soon.
"We believe that this will be resolved long before the November election," Austin said.
The state controversy has already trickled into the national limelight, and could worsen the perception of Illinois politics or "Chicago-style" politics that Republicans have assailed. But it's unclear whether it will have any impact on the Democrats' national agenda or the November elections.
"I don't think that it's going to have an electoral impact outside of Illinois in November," Gonzales said. "I think that this election is going to be about broader themes on economy [and] direction of the country."