Friday's session lasted for approximately 30 seconds.
"Senate Democrats will filibuster their own bill," McConnell's spokesman said.
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.