CHICAGO (CBS) -- Some of the staff in Illinois Gov. JB Pritzker's inner circle met with Chicago Bears executives Wednesday to discuss how the state might help fund a new stadium on the lakefront south of the present Soldier Field.

The meeting was not in person but virtual—and notably absent was Gov. Pritzker himself. Chief of Staff Anne Caprara and Deputy Gov. Andy Manar were present for the virtual meeting.

Pritzker has expressed doubt that the stadium plan would be a good idea for Illinois taxpayers. Now, it is up to the Bears to convince the governor's team otherwise.

It did not seem Wednesday afternoon like the Bears had succeeded in that mission.

In a statement, Pritzker's press secretary said:

"As the Governor has said, the current proposal is a non-starter for the state. In order to subsidize a brand-new stadium for a privately owned sports team, the Governor would need to see a demonstrable and tangible benefit to the taxpayers of Illinois."

"The Governor's office remains open to conversations with the Bears, lawmakers, and other stakeholders with the understanding that responsible fiscal stewardship of tax-payer dollars remains the foremost priority."

The public announcement of the plan for the new stadium last week was presented with excitement from Bears President Kevin Warren and Mayor Johnson, who promised that Chicago taxpayers would not be on the hook for the bill.

But Gov. Pritzker was not so enthusiastic.

"I remain skeptical about this proposal, and I wonder whether it's a good deal for the taxpayers," Pritzker said last week at an unrelated event before the Bears' formal announcement. "It's very important to me that, with all that the state needs to accomplish, that we think about what the priorities are of the state."

The project is not just the stadium itself – with a dome to cover it. It also includes the surrounding park area and infrastructure around the Museum Campus.

The new stadium is projected to cost $3.2 billion. Of that, $2.3 billion is coming from the Bears—including a $300 million loan from the NFL. The Bears will also seek public funding through 40-year bonds issued by the Illinois Sports Facilities Authority, or IFSA, which helped fund the 2002 renovation of Soldier Field—as well as the construction and renovations of Guaranteed Rate Field, the home of the White Sox. 

The surrounding infrastructure is expected to cost $1.5 billion, for a grand total of $4.7 billion.

Originally, the Bears planned to ask the State of Illinois for $900 million in IFSA bonds, which should eventually be paid off by the state's 2% hotel tax on gross hotel receipts.

The problem is experts say that type of contribution would take years to pay off.

"The financing upfront is very valuable to the team because it's going to be hard to come up with $900 million on their own, and then the public contribution is sort of spaced out over time," said Justin Marlowe, a research professor at the University of Chicago's Harris School of Public Policy and director for the Director of the Center for Municipal Finance. "To borrow that much money, given the revenues that they know they can collect from the hotel tax, you'd have to really stretch that borrowing out for about 40 years."

It is still not clear how the Bears plan to pay for the remaining infrastructure costs. They previously asked the city to ask the state or federal government for those funds.

No answer has been specified as to a plan B if the state or federal government says no.