Well first off, trying to be too strict about terms such as 'Lead Engineer' is pointless because different employers/industries/locations... will call the same thing different names (a rose by any other name...) so anyone getting upset over related issues probably wants to step back, take a deep breath & count to 10. Sure Radford Salary scale (or similar) which I believe feeds the categories seen on sites like Salary.com attempts to standardize job definitions but nothing forces companies to use the same definition. Likewise some large organizations have fairly well defined job duties etc. but they don't necessarily apply outside of those organization.
For instance to me the difference between 'Lead Engineer' and 'Engineering Manager' has bugger all to do with length of service and everything to do with the job role. To me Lead Engineer implies some kind of primarily technical lead, while Engineering Manager implies someone that primarily manages Engineers. However, that's my definition based on my experience and I don't necessarily expect it to apply to other people.
Back to the OP, there have been a bunch of threads about how to get first job for new grads etc. If you want to show some initiative as Triangled suggests then go look through them, see what you can learn and then maybe come back here post what you think you've learned and see what folks have to say about that.
Few comments, I got my first job by looking through the membership section of a relevant Industry organizations directory at the local library and sending hard copies of my resume with a cover letter to any companies that looked remotely interesting. One of those letters landed on the desk of the technical director the very day they were going to run an add in the local news paper to fill a position.
So don't just apply to posted job adds, apply to any potential employer.
My second job actually came from having my resume on one of the job websites - so they aren't completely useless but certainly shouldn't be your only or even your primary approach.
However, just because those approaches worked for my doesn't mean they'll work for you, and just because some approaches haven't worked for me doesn't mean they wont for you. For instance I've found 'pounding the street' pointless (if I'm lucky someone will actually take my resume and give me a business card and tell me to apply to their online recruiting website or similar) but many others swear by it and I'm not going to suggest they're wrong.
Posting guidelines faq731-376 (probably not aimed specifically at you)
What is Engineering anyway: faq1088-1484