Senate Democrats plan to introduce a no-confidence resolution in Gonzales in Washington this week.
"I have a sense ... that before the vote is taken, that Attorney General Gonzales may step down," Specter told Bob Schieffer on CBS' "Face The Nation." "Votes of no confidence are rare ... And I think historically, that is something which Attorney General Gonzales would like to avoid."
Specter said he would not "tell the president what to do ... We have separation of powers."
"I see no strong support for the attorney general within the Republicans, said Sen. Diane Feinstein, D-Calif., who is introducing the no-confidence resolution, adding that six Republicans had called for Gonzales to quit.
"I think there is an acknowledgement that he is a weak attorney general," Feinstein said.