According to the
Digest of Education Statistics for 2006 (tables 287 and 288), there were 6,601 doctoral degrees in engineering issued during 2004-05, including
1,566 in EE
915 in ME
773 in ChE
713 in CE
Those four disciplines represent 60% of the reported total, the rest were presumably in other engineering disciplines.
For comparison, there were 43,423 JD degrees and 15,461 MD degrees issued in 2004-05.