At issue are scheduled Saturday votes on the new strategic arms treaty with Russia, repeal of "don't ask, don't tell" and immigration.
"The treaty will require 60 votes to get cloture and ultimately 67 to be ratified. And I simply don't know the outcome of that," McConnell told conservative talk show host Sean Hannity.
The Kentucky Republican said he cannot predict the outcome on a bill to repeal "don't ask, don't tell," which prohibits gays from serving openly in the military.
McConnell said he is pretty sure Republicans can block the DREAM Act, which would confer citizenship on children who were brought illegally to the United States by their parents but who graduated from high school and attended college or joined the military.
The Hill reported Sen. Bob Corker, R-Tenn., warned Majority Leader Harry Reid's decision to schedule votes on the DREAM Act and "don't ask, don't tell" has had a "chilling effect" on the New START.
"I'm hoping that those will be taken down or else I don't think the future of the START treaty over the next several days is going to be successful, based on what I'm watching," Corker said.
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