Tesla77-
It is generally understood by employers that an ASMET or BSMET both lack the rigor of an ABET-accredited mechanical engineering program (BSME). The associates degree certainly doesn't hurt but it doesn't carry the weight of the BSME nor does it signify that you have completed the rigorous subjects of mechanical engineering (calculus-based physics, thermodynamics, fluid mechanics, strength of materials, heat and mass transfer, et. al.)
On the other hand, I have worked with guys with no degree at all that managed to work their way up to an engineer title. These guys invariably started out as draftsman, were promoted to designer, then finally promoted to engineer. Even so, these guys never had the ability to do quantitative analysis (e.g. heat transfer, stress/strain analysis) and were never given that kind of work.
Tunalover