Durbin was referencing Rosa Parks, an African-American civil rights activist who was arrested for refusing to give up her seat on a bus.
The office of Senate Judiciary Chairman Chuck Grassley (R-Iowa) pushed back, arguing Democrats could have made Lynch’s nomination a priority late last year when they still had the majority.
"The remarks made this morning by the Democratic leadership were misguided, shameful and, as their own record in the majority shows, hypocritical," Grassley’s office said in a statement.A vote on Lynch could be delayed until April if it does not take place next week. The Senate is set to go on a two-week recess one week from Friday.
McConnell said Tuesday that Lynch will get a vote, it's just a matter of when the Senate passes the human trafficking bill.
Durbin suggested that Republicans are using the vote to "target" Lynch.
"Why has the Senate Republican leadership decided to target this good woman and to stop her from serving as the first African-American attorney general of the United States of America?" Durbin said. "There is no good reason."
With unanimous support from Democrats, Lynch would need four GOP votes to be confirmed. Republican Sens. Jeff Flake (Ariz.), Susan Collins (Maine), Lindsey Graham (S.C.) and Orrin Hatch (Utah) have suggested they will back her.
Updated at 5:22 p.m.