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Complicating things for Mr. McDonnell, his office had to beat back sudden rumors over the weekend that he was about to resign after the conservative blog Bearing Drift said a plea deal involving a resignation was in the works.

On Monday, Mr. McDonnell told WWBT-TV in Richmond that such resignation claims are a “really, really bad rumor that you shouldn’t pay attention to.”

And despite issues with Mr. Williams and Star Scientific Inc., the nutrition supplement company he runs, recent opinion polls show Virginia voters still giving Mr. McDonnell high marks.

In polls since May conducted by The Washington Post, NBC/Marist and the Democrat-leaning Public Policy Polling firm, Mr. McDonnell has averaged a 56.3 percent approval rating compared to a 29.3 percent disapproval rating — a net positive of 27 percentage points.

Not so fast, Mr. Goldman said.

“Anybody who thinks they know how this thing will turn out politically ” he began, before trailing off. “Everything depends on what the facts are.”