The two amendments would alter the treaty, effectively killing the accord as it would send it back to negotiators. Democrats were likely to prevail in defeating the two measures.
Obama and Russian President Dmitry Medvedev signed the accord — it is known as New START — in April. It would limit each country's strategic nuclear warheads to 1,550, down from the current ceiling of 2,200. It would also establish a system for monitoring and verification. U.S. weapons inspections ended a year ago with the expiration of a 1991 treaty.
Proponents of the treaty, including much of the military and foreign policy establishment, cite the renewed weapons inspections and say the pact would keep the two biggest nuclear powers on the path to reducing their arsenals. Opponents assert it would restrict missile defense and argue that it has insufficient procedures to verify Russia's adherence.
Several Republicans said Obama's letter to congressional leaders Saturday vowing to move ahead on missile defense carried considerable sway.
"It takes care of me," said Sen. Robert Bennett, R-Utah, who indicated he was leaning toward voting for the treaty. Snowe said it was "important for the president to be emphatic with respect to missile defense and modernization" of the remaining nuclear arsenal. Voinovich welcomed the statement.