Sen. Marco Rubio (R-Fla.) Sen. Marco Rubio (R-Fla.).

Sen. Marco Rubio (R-Fla.) on Sunday reiterated concerns with the bipartisan immigration bill he helped author, saying the measure needs strengthened border security components to win passage in both chambers of Congress.

"I think it's an excellent starting point," Rubio said of the bill on "This Week With George Stephanopoulos." "I think 95, 96 percent of the bill is in perfect shape and ready to go. But there are elements that need to be improved."

Rubio repeated his assertion that the bill needs beefed up border security provisions to win passage.

"The only way we are going to pass an immigration reform law out of the House and the Senate so the president can sign it is if it has real border security measures within it," Rubio said.

"If the bill stays as it is regarding border security, do you vote for it?" asked ABC's Jonathan Karl.

Rubio responded: "Listen, I'm -- I don't really want to get involved in these hypotheticals and ultimatums about what I want."

Rubio also responded to conservative critics who have taken him to task for supporting comprehensive reform. "The reason why I've undertaken this is because this is a major problem that's hurting out country," Rubio said.

The Florida Republican said he didn't catch President Obama's speech on immigration reform last week.

"I didn't quite frankly even hear the speech," Rubio said.

Sen. Lindsey Graham (R-S.C.), who like Rubio is part of the bipartisan "Gang of Eight" that crafted the immigration bill, was bullish Sunday about its prospects for passage.

"I think we are going to get plus 70 votes" in the Senate, said Graham, who predicted a "political breakthrough, that Congress is going to pass immigration reform."

Updated at 11:38 a.m.