Sen. Joe Lieberman (I-Conn.) said the administration may have problems getting the START treaty signed last week ratified in the Senate.

Lieberman said he'd arrived at his belief on the vote tally falling short after conversations with colleagues over the congressional recess.

"I don't believe that there will be 67 votes to ratify the START treaty unless the administration does two things," Liberman said on "Fox News Sunday." "First, commit to modernize our nuclear stockpile so as we have less nuclear weapons we know they're capable, if, God forbid, we need them; and secondly, to make absolutely clear that some of the statements by Russian President Medvedev at the signing in Prague that seem to suggest that if we continue to build the ballistic missile defense in Europe that they may pull out of this treaty -- they're just unacceptable to us.

"We need that defense to protect our allies and ourselves from Iran," Lieberman said.

President Barack ObamaBarack ObamaOvernight Finance: GOP divided over welfare cuts in budget | Lawmaker loses M on pharma stock he pitched | Yellen says another financial crisis unlikely in our lifetimes Why UK millennials voting for socialism could happen here, too Overnight Regulation: EPA moves to repeal Obama water rule | Labor chief to review overtime rule | Record fine for Google MORE backed away from the controversial missile shield, a plan launched under President George W. Bush, at the beginning of his term, earning kudos from Russia but disappointment from Poland and the Czech Republic.

Lieberman stressed that as stockpiles are slashed, "we have to make darn sure that our nuclear warheads are capable, are modern. And a lot of them are decades old."

"Fox News Sunday" host Chris Wallace asked Sen. Lamar AlexanderLamar AlexanderThe Hill's Whip List: GOP undecided, 'no' votes pile up on ObamaCare repeal bill Trump administration pays June ObamaCare subsidies to insurers Republicans and the lost promise of local control in education MORE (R-Tenn.) about the chances of getting nine Republican votes need in the Senate to ratify the treaty.

That depends on the administration's answers to the concerns posed by those like Lieberman, Alexander said.

"I mean, reducing the number of nuclear weapons that are deployed to 1,500 gives us plenty to blow everybody to kingdom come if that's what we choose to do," Alexander said. "But the questions are some of the ones mentioned by Senator Lieberman, and we need to take plenty of time to answer them."

Alexander also took issue with Obama's "troublesome" Nuclear Posture Statement, which declared that the U.S. wouldn't hit a non-nuclear country with nuclear weapons.

"It takes away the ambiguity about our use of nuclear power," Alexander said. "Ambiguity in foreign policy is sometimes very useful, as we've found."