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."
Shelby is "holding hearings to determine where legislation is needed."
The Senate's No. 2 Republican backs plans for a vote next week.
Vocal Kremlin critic Boris Nemtsov was shot in Moscow last week.
Conservative groups had urged lawmakers to oppose the bill, which passed 316-101.
The New Democrat Coalition calls for fixing the tax code and raising infrastructure spending.
Nelson said he was "assured" the bill would not come up before the March 24 deal deadline.
Senators will vote a day sooner as a snowstorm heads for D.C.