I am trying to learn as much as I can about portrait/people/wedding type photography and would very much like to work/assist some local professionals that do this type of work so that I could hopefully learn this business. Is this something that I could reasonably expect a professional to do or am I fighting an uphill battle?
You could probably be taken on for a couple shoots as free labor ("hold this, carry this, fetch this..."), then potentially work as a paid assistant once you've proven your value and client-appropriateness. I'd call and email around to local working pros and offer yourself up. Just don't carry in a portfolio or hype up your own shooting - they aren't going to care if you can take a nice photo, they're going to care if you can be johnny-on-the-spot and keep your mouth shut in front of clients.
No one plans on being an assistant forever - it's a bit of a given that assistants plan on cultivating their own photography career. I've heard of pros referring jobs that they're unavailable for or too expensive for to current and ex-assistants.
That said, if you're trying to juggle this around a full-time job or only plan on being available sporadically then don't bother. Speaking from personal experience, I have no interest in putting in the time and effort to cultivate freelance talent if they're going to be dilettantes and never available when I call with a gig. If I call with a job and someone's unavailable three times in a row I bump them down to the bottom of my freelancer list.
Apprenticeship is a well-established practice in the wedding/portrait world. Its sort of assumed that any assistant/second-shooter worth having will likely want to strike out on their own eventually.
As shatter said, expect to be free/cheap labor at first until you establish your value. However, I personally take my responsibility to any free/cheap "interns" very seriously in terms of training... and ensure that they are more than getting their time's worth.
Like Evan said, apprenticeship is a good way to get the background experience you need. Be prepared though for the search to find that position. Currently there is an army of aspiring folks that are willing to carry bags for established pros. Only problem is, not enough pros to go around in some markets. Be patient and persistent and you will find someone willing to take you on. Once you do ... heed Simon's advice. Be available, show up on time and ready to work. The rest will fall in to place.
When I did wedding photography, I used assistants. I used some who are like you, interested in the business. I used others, like our receptionist who needed some extra money, to help me. They had no interest in photography.
Generally, I was more pleased using the latter than the former. I was more interested in assistants I could tell: "Go there. Hold this. Carry that.", and they would; swiftly, efficiently, quietly and without question. Wannabes were usually more interested in learning than helping.
Even back in the 80's, every week I'd have two or more guys or gals just like you come to the studio and ask to assist. I can only imagine what it's like now. I understand business is off in general. If you find this a tough nut to crack, it's not necessarily you.
I appreciate you wanting to assist and learn the business before going into business. I had a student in an intro to digital photography workshop I taught who already had business cards and a web site. She had weddings booked and she had never photographed or assisted at one. Oh my!