Feinstein added in the wake of the allegation the FBI needs to investigate Kavanaugh's background and if the White House refuses to ask the FBI to investigate the Judiciary Committee "must subpoena all relevant witnesses."

"It is time to set politics aside. We must ensure that a thorough and fair investigation is conducted before moving forward," Feinstein added.

The California senator was more explicit in a separate tweet, saying Thursday's hearing "should be canceled in light of a disturbing new allegation of sexual misconduct against Brett Kavanaugh. The FBI must investigate ALL allegations."

In addition to Feintein, Sen.(D-Calif.) said the FBI needs to investigate and that Mark Judge, a Kavanaugh classmate, "must be compelled to testify" before the Judiciary Committee.