"I never was in favor of shutting down the government. I was never in favor of defunding the government," he said. "The only thing I didn't want to see us is us waste any more money on is Obamacare [Affordable Care Act], which is proven to be a disaster."
Rubio was one of 18 Republican senators who voted against the deal to reopen the government and put 800,000 furloughed employees back to work.
He said that the Democrats in the Senate, who did not negotiate on the funding of Obamacare, are responsible for the shutdown.
"They took that position and they forced this situation that we have just gone through," he said.
Rubio also criticized the secretary of Health and Human Services, Kathleen Sebelius, for not testifying before a House subcommittee on the problems with the Obamacare roll out.
"Her refusal to testify and be transparent ... is undermining her credibility," he said. "And there may come a point now ... where, in fact, she will have to resign largely because she no longer has the credibility to do the job."
Rubio also noted that administration officials have announced that 476,000 people have applied for Obamacare.
There is no notion of how many people have been deemed eligible and enrolled, however.
"They need to get 7 million people on this thing," he said. "There is a lot of work to be done in terms of getting other people on there, and there is no mechanism for them to be able to do that."