(CBS) – Gun violence, Syria and an impression of Bill Clinton highlighted a nearly 15-minute long appearance by Chicago Mayor Rahm Emanuel Monday on the Late Show with David Letterman on CBS.

The mayor also talked about running for a second term, and offered insight into the decision making currently underway at the White House surrounding the crisis in Syria.

“What I hear about Chicago now is don’t go to Chicago, the violence is unbelievable,” Letterman said to Emanuel. “Now, tell us why people say that.”

“Well, first of all they’re watching CBS and you late at night,” responded Emanuel about the level of crime. “Actually it’s on its way down. We’re down 24-percent on shootings.”

Emanuel did not touch on the high murder rate, which included 53 homicides in August and 48 in July.

The mayor also said that Letterman’s home state of Indiana is one of the sources of illegal firearms flowing into Chicago.

“I don’t know if you know this, that thing next door called Indiana, they kind of come flowing in once in a while. What you need is what the President proposed, which is a universal background check,” he said.

Emanuel’s appearance on the Late Show coincides with the debut of a Discovery Channel documentary about presidential chiefs of staff called “The Presidents’ Gatekeepers” in which Emanuel is featured prominently. Before being elected mayor, he served as President Obama’s chief of staff and as a senior advisor to President Clinton.

As he welcomed Emanuel, Letterman joked about how mayors in Chicago have had the same last name for decades.

“When I was a kid, the mayor of Chicago was always named Daley, and then there was Jane Byrne for a while. What happened to the juggernaut powerhouse Daley regime because his son was mayor for a while … in fact you took over after him didn’t you?” Letterman asked.

“Your American history is unbelievable,” Emanuel told Letterman. It’s time for a new chapter, it’s time for some changes. Both Richard Daley – his father and himself have done great things for the city, but it’s time to get the city moving and on a new chapter.”

On the subject of Syria, Letterman asked Emanuel. “Do you wish you were the chief of staff now?” Emanuel quickly replied, “No.”

And as his former boss prepares to address the nation on Syria, Emanuel told Letterman, “This is not an easy choice. He knows the country is not behind him but he knows what he thinks is right. I think the Congress of the United States should make sure America stands tall at this moment.”

Emanuel also told Letterman what everyone already knows, that he does plan to run for a second term in 2015.

That prompted this follow-up from Letterman, “If you weren’t campaigning, would you rather be with the president right now?”

As the audience laughed, Emanuel responded, “First of all, I’m not campaigning for 16 months and the answer to that is still no.”

“I loved being senior advisor, loved being a Congressman and loved being chief of staff. Being mayor is the greatest job…the best job I’ve had in public life. I am proud I got to serve my country … but I love being the mayor of a great city and being able to do things that I think are really great,” he added.

Asked what he might do after being mayor, Emanuel joked, “I was thinking of this late-time talk show thing.”

Referring back to his job as President Obama’s chief of staff, Emanuel called it “the most intense job you’ll ever have.” He talked about the struggles of Mr. Obama’s first months in office.

“He walked in and he had two of the longest wars in American history, the great recession, the financial meltdown and the auto industry on its back and near collapse. And that was day one on the inbox. And you have to help formulate a strategy…and you don’t walk into the Oval Office with a problem unless you’ve got one or two solutions.”

As he ended the interview, Letterman said to Emanuel, “I noticed you’re missing a finger.”

“Your ability to catch the obvious is unbelievable. But you know it gets you special parking,” the mayor responded.

“The Presidents’ Gatekeepers” documentary about White House chiefs of staff will air on the Discovery Channel in two parts on Sept. 11 and Sept.12.

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