It has been a few years... But at least in the SF Bay Area, it was getting harder and harder to get a mechanical engineering job with just a BS...
I understand wanting to get out and work (I did between HS and College). And, from what I have seen, it is very difficult for someone that has been working to get back into college again (bills, married, etc.).
In general, I am a big believer in engineers getting some practical experience--too many engineers I have seen have very little common sense when it comes to try and solve problems and foresee issues.
Yes, getting experience in one or more CAD / Solid modeling software packages is pretty much a requirement these days--I was also suggesting some programming knowledge too. Learning C, scripting, and/or other languages associated with a Solid Works / AutoCAD / ProEngineer type package will really be a help when it comes to generating documentation packages and undertanding how to interface with Machining Centers, Simulation Packages, and even the (seemingly simple requirements) of documenting to archive and creating packages for vendors.
In the old days (30+ years ago), an engineer who did not know these things would just have a drafting department of junior engineers / draftsperson / specialists for support. Today--the best engineers (I have seen) are able to "do it all" and understand the requirements of their "customers". I have had, otherwise very smart designers ignore the requirements of the outsourced vendors (and even tell me that the vendors are wrong)--and I have had outsourced ME/CAD vendors lose very lucrative contracts when they turned simple designs over to a senior drafts person who knew how to drive a mouse but knew nothing about modeling, scaling, and not to use sample fastener drawings that came with the CAD package (drew a complete inch based design using mm units--19" rack mount computer was 19mm wide--sample fasteners did not match dimensions of real fasteners--not enough metal to even swag them in--sheetmetal shop went nuts when they got the model files to unfold the sheetmetal for fabrication. Drawings looked fined, but the models were just a bit larger than a postage stamp--required 100% redrawing / redesign by our internal designer to fix the problems).
Very few smaller companies can absorb the overhead of a support department--and if downsizing occurs, those that require support personnel are not going to last long.
Lastly, when you get the good job--save your money so that you have 6-12 months of savings to live on (keep your expenses low). Allows you to enjoy the job more and have more choices in life (try new job, leave job where they treat you like poop).
My two cents worth. Good Luck and have Fun!
-Bill