Top officials from the State and Defense Departments are expected to testify.
Sen. Patrick Leahy called his proposal a fitting tribute to "Bloody Sunday" marchers.
The Department of Veterans Affairs has more than 214,000 backlogged disability claims.
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.