The endorsement puts further pressure on Democrat P.G. Sittenfeld to back out of the race.
Progressive favorite's decision sets up primary fight with Rep. Chris Van Hollen and others.
GOP congressman would consider run if Rubio tries for White House.
Alaskan had the lowest 2014 score of any GOP senator, and the group could primary her.
Stephanie Rawlings-Blake could be the second female African-American Democrat in the race.
The Maryland Democrat will reportedly announce her candidacy on Tuesday.
“Ted Strickland is a champion for middle class Ohioans," Sen. Sherrod Brown said.
Republicans are defending 24 seats compared to Democrats' 10 in a much more favorable 2016.
"I enthusiastically endorse Chris Van Hollen," the Senate Dem leader said.
The Maryland Democrat is already facing resistance from MoveOn.org and others.