There's "not a chance" the U. S.-Russian arms-reduction treaty would win Senate approval this year, Sen. Lamar Alexander, R-Tenn., said on Sunday.

Alexander said on "Fox News Sunday", "With the Supreme Court pushing to the front of the agenda in the Senate and jobs, terror and debt being our major issues we should be worrying about, this is a treaty for next year."

Alexander, the third-highest ranking Republican in the Senate, said, "There's not a chance the treaty will be approved this year."

A deal with Russia to cut nuclear arsenals and new limits on the use of U. S. nuclear weapons won't pose security risks, the Obama administration said on Sunday.

President Barack Obama signed the arms-control treaty with Russian President Dmitry Medvedev Russia Tuesday. The same day, Obama unveiled a new nuclear strategy that says the United States would not use nuclear weapons against a non-nuclear country in compliance with non-proliferation agreements.

It has been reported that the administration's Nuclear Posture Review labels nuclear terrorism the greatest threat to U. S. and global security, and Obama said security for the United States and its allies can be increasingly defended "by America's unsurpassed conventional military capabilities and strong missile defenses."

Obama would have trouble winning Senate approval of the treaty unless the administration pledged to modernize the U. S. nuclear weapons stockpile, said Connecticut Independent Sen. Joseph Lieberman, also appearing on Fox.

Lieberman further said, "As we reduce the number of nuclear warheads America has in a world that is still dangerous, very dangerous, and in which the threat of the spread of nuclear powers, particularly Iran, grows every day, we have to make darn sure that our nuclear warheads are capable, are modern." (With Inputs from Agencies)