When asked if he had the votes, Obama replied, "I'm confident that we should be able to get the votes."
Ratification would require 67 votes in the 100-member Senate. Once the newly elected Senate is seated in January, Democrats will need the support of at least 14 Republicans.
"This is not a Democratic concept. This is not a Republican concept," Obama said. "This is a concept of American national security that has been promoted by Ronald Reagan, George H.W. Bush, Bill Clinton, George W. Bush and now my administration. We've taken the time to do this right."
The agreement would shrink the U.S. and Russian arsenals of strategic warheads to 1,550 for each country from the current limit of 2,200 and revive on-the-ground inspections that ceased when a previous treaty expired nearly one year ago.
Republicans argue that the treaty would limit U.S. defense options and does not provide adequate methods to make sure that Russia is living up to its terms.
The Associated Press contributed to this report.