Sen. Marco Rubio: I Back Tighter Border Security

In an interview on Sean Hannity's radio show Wednesday, Republican Sen. Marco Rubio of Florida said he would support a House immigration plan that tackled the single issue of border security, but admitted more had to be done to fix the U.S. immigration system.

Rubio made it clear he had "no problem" backing a bill dealing solely with border security, but knows that's just one piece of the puzzle.

"Well yeah, but at the end of the day border security is an obligation of the federal government no matter what your illegal immigration problem may be," Rubio said. "Even if you didn't have a single illegal immigrant, you'd still have to have effective border security because it goes down to your sovereignty. So I have no problem with doing border security. That alone won't solve our immigration problem, however."

Rubio told Hannity that before anyone who is in the country illegally is given permanent status, border security is job No. 1.

"In the interim, while you're doing the border security, you have to account for the people who are here illegally, and that's why the bill gave them a temporary status," Rubio said. "Now the argument is, is it really temporary? Because once you give something, you can't take it back.

"But again, I would just argue to you that the only difference between what they have now and what they would have under the bill is at least we'd know who they are and they'd have to be paying taxes."