I'm about to become a mechanical engineering graduate (hate the field). I am familiar with Python, Lisp, Haskell, C++, C, and JavaScript. Is there any alternative to spending months to develop a portfolio of project/s to get employed in the web development field?

You will easily get a job in the software industry, if you have interest and knowledge of the languages you have mentioned. Trust me, many people from the cse field don't have this much knowledge when they appear for campus interviews but they learn once they are in the job. Its an advantage you have prior knowledge. Campus recruitments are not that hard, they don't expect you to be a master of everything. My advice, try to get a job in a startup, they wont care from what field you are, they will only judge you by your knowledge.

There are some people who studies CSE/ECE without having proper knowledge and who can't even solve a simple problem get jobs at a software based company. Their intentions of studying in this group because they think it's cool. But you sound total different you seem like a geek. If you appear on an interview you can surely secure a good job and of course you can go to a better position very sooner. You can even go further and build something on your own, like an app or open source project and make it as your profession. It requires great courage and sacrifice to achieve it.