"And in the months to come, I'm really going to focus on the issue of repealing ObamaCare, because in addition to the IRS's role, there is all sorts of other problems with regards to ObamaCare that we need to answer."

Rubio has been criticized in recent weeks for favoring an immigration reform bill that many Republicans say would create a pathway to citizenship for millions of illegal immigrants and require people to trust that the government would crack down on illegal border crossings.

On ObamaCare, Rubio's comments were much more in line with those of other Republicans. He said the IRS scandal shows the IRS is either "targeting people because of their political views, or is incompetent."

He said Americans should be "very concerned" that this same IRS will have a leading role in enforcing ObamaCare.

"The IRS is going to go through the country asking people … 'Prove to us that you have health insurance. Prove to us that the health insurance you have is adequate and, if you don't have health insurance, pay us $2,000 or a similar fine or fee or tax as a result of failing to get health insurance,' " Rubio said.

He said repealing the 2010 healthcare law is needed because either the IRS will enforce it, or a new agency will be needed to enforce it.

"One of the things that separates America from the rest of the world is that our founders knew from history that no matter who's in charge of government, if that government gets too big and too powerful, it will abuse that power," Rubio concluded.

"Well, we're seeing evidence of that here now with the IRS. We need to remember our constitutional founding principles of limited government because they are the right thing to do for our country. They are a distinguishing feature of this land, and we can never afford to lose that."