"The truth of the matter is that the current leadership of the Senate doesn't allow any votes on anything. You can't file an amendment. I, as a member of the minority party, by saying, 'I'd like to file an amendment to the bill' — they won't let me get a vote on it, until last week when they specifically lined up 78 votes to avoid my ability to come on your show," he said.
"They did that just to block you from coming here?" Stewart asked.
"Yeah, I think so," Rubio said.
Rubio was set to join "The Daily Show" last Tuesday, but his media appearance, as well as a book event at the National Constitution Center in Philadelphia, were canceled because of Senate voting, said his press press secretary, Alex Conant, according to the Philadelphia Inquirer.
Stewart questioned Rubio on what he said was excessive use of the filibuster by Republicans in the Senate, leading Rubio to create some of his own language to describe the situation.
"On the filibuster, that's ... really Senate-y-ish. Is that a word?" said Rubio.
"If it isn't, it is now," responded Stewart.
In a sprawling interview that ran more than a half-hour, Jon Stewart tried to press Rubio on Republican obstructionism, while the Florida senator deflected criticism and promoted his views on immigration, taxes and the federal deficit.
Rubio, an outspoken advocate for immigration reform, continued to accuse both Republicans and Democrats of oversimplifying the problem.
"On the one hand we have to recognize that the people who are here, even if they're undocumented, are here because they're looking for a better life … on the other hand, we can't be the only country in the world that can't have an immigration system that's enforced," he said.
"It's a difficult balancing act," Rubio added.
Rubio, who has been repeatedly mentioned as a possible running mate for presumptive Republican nominee Mitt Romney, defended earlier remarks in which he called President Obama the most "divisive figure" in modern history.
"My concern is that the president [has] given up on the chance he had in 2008 to be different … I look at the president today and he's not the same person. He's become like everybody else in Washington. And he had a chance to be different, even though I disagreed with him," Rubio said.
When pressed on whether Republicans were also to blame, Rubio said, "I think politics today is divisive and certainly people pick on that, but I've called out my own party on that."
Rubio has been on a media whirlwind tour, promoting his new book, An American Son, which has spent eight days in the list of top 100 best-sellers on Amazon.