Former Illinois Gov. Rod Blagojevich told David Letterman he keeps thinking he'll wake up and people will realize "this is just one big misunderstanding."

The ousted governor showed on Tuesday up for a taping of CBS' "Late Show with David Letterman." He laughed with the audience when Letterman mentioned watching him on several television talk shows.

Letterman joked that the more Blagojevich talked and repeated his claims of innocence, the more the host said to himself, "Oh, this guy is guilty." Blagojevich said he appreciated Letterman's position but also believed he had to defend himself and assert his innocence.

Citing three previous Illinois governors with corruption convictions, Letterman joked: "Is this just part of the oath of office that you guys take?" Blagojevich replied, "Unlike those, I'll be vindicated," to laughter in the audience.about clearing his name.

Before Blagojevich's removal, Letterman listed the "Top Ten Ways Rod Blagojevich Can Improve His Image," which ended with, "Uhhh...resign?"

Blagojevich's latest round of national TV interviews Tuesday in New York also included a stop at FOX News' "On the Record with Greta Van Susteren."

His publicist insists the appearances are not about finding the former governor a new job.

But Blagojevich, a lawyer whose license is inactive, has some hurdles to overcome if he wants a new career. The biggest one: Who would hire him?

"A great many employers will not hire someone who has a felony charge pending against them," said Chicago defense attorney John Beal.

But some might offer him a job, if only to exploit the built-in publicity surrounding the scandal-tainted Democrat, especially as he gets closer to a trial on charges that could bring a lengthy prison term.

A federal indictment is expected by April on allegations that Blagojevich tried to auction off Barack Obama's vacant Senate seat. He was impeached by Illinois lawmakers, who stripped him of his job last week.

Blagojevich's publicist says offers are coming in, but he declined to provide details.

"Every day we get several offers of something he could do or would like to, and there are certainly no shortage of people who would love to speak with him," publicist Glenn Selig said.

Before the unanimous vote to remove Blagojevich, one Chicago radio show offered him a job if he would resign in the wake of his Dec. 9 arrest on federal corruption charges. He refused to step down.

The former governor needs find a way to make a living. Not only did he lose his $177,000-a-year job, but his wife recently was fired from her $100,000-a-year job as the chief fundraiser for a Chicago homeless agency.

Federal authorities claim she was caught on secretly recorded tapes making expletive-laden demands to fire Chicago Tribune writers critical of Blagojevich.

"It's a period of adjustment for us. But you know what, I'm not asking for any sympathy. There are tens of thousands of Americans who are losing their job every single day. I just happen to be among the ranks," Blagojevich told NBC's "Today Show."

The Illinois Senate convicted Blagojevich last week of abuse of power and removed him from office. He also faces federal charges including allegations he tried to profit from selling President Obama's U.S. Senate seat.

In addition to charges that he tried to personally benefit from his Senate appointment power, Blagojevich was accused of trying to strong-arm the Chicago Tribune into firing unfriendly editorial writers and of engaging in so-called "pay-to-play" politics in which state jobs or contracts are exchanged for campaign contributions.

If convicted, he could face a serious prison term. Conspiracy to commit fraud is punishable by up to 20 years and solicitation to commit bribery by as much as 10 more years. If he's hit with a racketeering charge, that could send him to prison for up to another 15 years, said Leonard Cavise, a law professor at Chicago's DePaul University.

The Associated Press contributed to this report.