The White House still thinks it has the Senate votes to put Chuck Hagel in the top job at the Pentagon, but concedes it would be a narrowly won victory.

After a confirmation hearing last week that did nothing to help Hagel’s candidacy, the Obama administration counts about 57 senators as supporting his nomination to lead the Defense Department. A handful more have said they would oppose a filibuster.

Hagel is continuing his Capitol Hill courtesy calls this week, scheduled to meet with roughly 20 senators, which would push his total to about 72, a senior administration official said.

And those meetings are said to have gone better than his public berating at the Senate Armed Services Committee.