The schedule change comes ahead of an expected snowstorm.
McConnell says there is nothing partisan about scheduling the vote.
Murkowski calls on colleagues to "embrace your inner-Arctic self."
Senators will vote a day sooner as a snowstorm heads for D.C.
"The Stand with Israel Act of 2015 sends a clear message," Paul said.
The Supreme Court is hearing oral arguements on a challenge to the health law.
Senators are expected to take a procedural vote Wednesday on overturning the veto.
Sen. Mitch McConnell (R-Ky.) said lawmakers could take up the legislation next week.
The Senate will vote to roll back a rule making it easier to hold union elections.
The legislation would let Congress weigh in on any Iran nuke deal.