The move is leverage to convince the North Carolina-based bank to use some of its federal bailout money to resolve the situation at Republic Windows and Doors.
The company closed last week with just a few days' notice.
Blagojevich says banks got bailout money and should provide lines of credit to businesses that need it so workers can keep working.
The announcement came after Blagojevich met with the workers on Monday.
"We expect these banks to bail out these businesses," the governor said, reports CBS Station WBBM.
The state also will get a federal court injunction Tuesday to make sure federal law is followed so workers get benefits like severance and vacation pay.
The move comes on the fourth day of a sit-in by more than 200 workers at Republic Windows, who have become a national symbol for thousands of employees who have lost their jobs as the economy continues to sour.
"What we really want here is to save the jobs. Because this is 300 people without jobs," mechanic Vincente Rangel told CBS News correspondent Dean Reynolds.
"We never expected this," said Melvin Maclin, a factory employee and vice president of the local union that represents the workers. "We expected to go to jail."
The employees were let go from their jobs last week with only three days' notice and no severance pay.
They claim this is a violation of the Worker Adjustment and Retraining Notification Act (WARN) which says employees must have 60 days' notice or severance pay in the event of a plant closing or mass layoff.
According to workers, the company can't pay them because their creditor, Bank of America, won't let them. The company told the union that Bank of America has canceled its financing.
The bank had said in a statement that it wasn't responsible for Republic's financial obligations to its employees.
The workers have consequently refused to leave until they receive their rightful benefits, and they are blocking the removal of any assets from the plant.
Illinois Attorney General Lisa Madigan said her office was investigating the company, which has not commented on the sit-in.
"The reason they're here is they've got nothing left to lose," organizer Leah Fried of United Electrical Workers told CBS' The Early Show. "They were told on Tuesday of last week they were out of a job on Friday and penniless on the street.
"People have been very strong, very united and they're not going anywhere until they win justice."
Bank of America (as Republic's creditor) now owns the company's assets. That, says Fried, makes them responsible. "These workers are owed their vacation pay and if this factory continues to stay closed, then they're owed 60 days' pay under the WARN Act."
Fried says Bank of America - which recently received $25 billion from the government financial firm bailout - should be held responsible. "I think we need to hold them accountable for what they do to our economy and whether or not they are investing in jobs, whether or not they're keeping people employed."
"That is not right to throw people out on the street with nothing," she said.
Fried said the laid-off employees are simply protecting the products of their labor. "There are hundreds of thousands of dollars' worth of windows in this company which are ready to be delivered [that] these workers worked to manufacture, [and] they're not getting paid," Fried told Rodriguez. "All they're simply doing is placing a lien for their work and saying let's respect the law.
"They worked real hard," she said. "We have workers here 34 years. They made this company the success that it is. And on the eve of Christmas, they shouldn't simply be thrown out on the street. And if the federal government can't intervene to protect these workers, then I think we're failing in our main obligation."
And how long will they stay at the plant? "As long as it takes," Fried said. "They're not giving up. They are incredibly strong and united."
Sen. Dick Durbin of Illinois said from the shuttered plant that he would talk to fellow senators about reminding banks that taxpayer dollars are not for dividends or executive salaries.
"We have been sending billions of dollars to banks like Bank of America, and the reason we have sent them the money is to tell them that they had to loan this money out to companies just like Republic so that we can keep these companies in business and not lose these jobs here in the United States," he said.
Rep. Luis Gutierrez, D-Ill., has organized a meeting between representatives of the union, Republic and Bank of America for 4 p.m. this afternoon. "We want to end the finger-pointing," he told The Early Show. "Whether it's the company or Bank of America, let's open up the books. The company has agreed to come and sign a release, a waiver, so we can look at the books and see where the money is at.
"Look, you guys are reporting on what we did for the financial industry," he said. "$700 billion, another $15 billion or $20 billion for the automobile industry. Who is standing up for workers? We think the federal government has to make sure that the WARN Act, which says that these workers are due 60 days of pay and health benefits, has to be enforced. Let's make sure the federal government does its job with these workers, not with just those on Wall Street.
"This is Main Street here."
"These workers deserve their wages, deserve fair notice, deserve health security," Jackson said. "This may be the beginning of long struggle of worker resistance, finally."
President-elect Barack Obama, weighing in on behalf of the workers, told a news conference Sunday that Republic Windows and Doors should follow through on its commitments to the employees.
"The workers who are asking for the benefits and payments that they have earned, I think they're absolutely right and understand that what's happening to them is reflective of what's happening across this economy," Obama said.
One of the factory's workers, Silvia Mazon, said in Spanish that she needs the money owed to her for an $1,800 monthly house payment. The 40-year-old from Cicero said she has enough money saved to survive for one month.
"We're making history," she said.
Rep. Jan Schakowsky, an Illinois Democrat, called it the start of a movement. "This story has resonated around the world," she said.