Hi and welcome to POTN,
Realistically, you would be very wise to work as a 2nd shooter for a while and learn the ropes. If you have a good mentor or two, that will make your transition much, much easier. Look for an established, successful shooter who is willing to pay reasonably for a 2nd. Get permission to use your images in your own portfolio and be careful about overly restrictive non-compete contract clauses.
I would not recommend going into debt or quitting your day job yet. Eventually if you have a really solid business plan and are very certain of your market potential and have done a cost of doing business analysis and developed a workable business plan, a loan is a possibility. But you really don't want that hanging over your head until you know a lot more about the business than you do now.
Shoot as a second, grow your equipment gradually, learn the business... Then in a few years you might be ready to strike out on your own.
$2000 is nothing. I'd estimate starting from scratch and wanting to go directly to shooting as the primary at weddings as your occupation, you would need at least 10X that much just to buy equipment (and probably at least another $20K-30K to live on for the first year or two until you start to turn a profit... maybe more if cost of living is high in your area).
You need two cameras... minimum. Probably the best models currently for wedding photography - all things considered, including value - would be 5DII. The 5DII excels because it's full frame (maximum control over depth of field is desirable for portrature) and because it's very capable at higher ISOs. A very doable second best: 7D. A 60D might serve too... It's a lot better camera than most people give it credit for being. 1D Mark III/IV and 1Ds Mark III are perhaps the most ideal, for those who have little or no budget restrictions.... These would be the most cost effective for heavy, rigorous use. 7D is next in this respect, 5DII is third and I would guess about the same as 60D. But keep in mind that you'll need two cameras. You cannot afford to miss an event because your one and only camera is broken.
Lenses are even more critical than the camera(s) you choose. The lens can determine your particular "look" and you need good, reliable ones that can give you solid results in difficult shooting situations. Canon 24-70/2.8L is one of the most popular for wedding photogs. The 24-105 is another that some like to use, but for portraiture a larger aperture is often better. A 70-200/2.8 IS is another, but instead of zooms some choose to use prime lenses such as 50/1.4 or 50/1.2L, 85/1.8 or 85/1.2L, 135/2L. No, "cheap" or entry level lenses such as the 50/1.8 II or the kit zooms are not a good idea mainly because they will not hold up to rigorous use... Get at least the 50/1.4. You want to avoid equipment failures as much as possible when shooting once in a lifetime events. Also, if Uncle Bob shows up with better camera equipment than you, you'll look pretty silly (although Uncle Bob likely doesn't know how to use it very well). You might also want a wider lens, as well... such as a 17-40/4L or 16-35/2.8L II, or primes like the 20/2.8, 24/1.4L, 35/1.4L (the latter two are really only wide on full frame cameras).
You will probably want to adapt this lens list a bit, if you choose to use a crop sensor camera such as the 7D or 60D instead of FF 5DII. Another approach is to have one (at least) of each, a full frame camera and a crop sensor camera, because this "leverages" your lens kit to be more useful.
You also need a minimum of two flashes. There are various ones available, Canon's 430EX would likely be the minimum requirement. An accessory battery pack can be important to keep you shooting through the entire day, with minimal interruptions.
Then there are all the specialty items to consider, that help you stand apart from other photographers and offer customers more reasons to choose you over the competition. Some sort of portable studio lighting might be desirable to do more formally posed work on location. A macro lens might be needed for cake, bouquet, and ring close-ups. A macro flash might be needed. A Tilt-Shift lens can be useful for front of the church shots, or for unusual shallow but controlled DOF effects. I consider ultra large aperture lenses such as the 50/1.2L and 85/1.2L II as somewhat specialized tools, too. None of these things are cheap, and you probably just need good, solid "basic" lenses to start out.
You have to know how to use it all under pressure, without missing a beat. You should be completely familiar with the various exposure and focusing modes of your chosen camera(s), when, where and how to use them. You have to anticipate and be ready to get the shot. In a sense, the photographer becomes the choreographer of a wedding. A wedding is no place to learn your craft or experiment until all the customer's required shots are in the can, each and every one done right.
Yet, the creative side is only a smaller part of the equation.... probably somewhere between 10 and 25%. The other 75 to 90% is the business side, and this is where even some of the most talented photographers fail. Negotiation, sales & marketing, customer interviews, legal aspects, bookkeeping, pricing, order fulfillment, quality control, follow up, business planning and many other details that don't involve camera and lens at all will usually be your very biggest concerns.
There is a wedding specific forum here on POTN.... I suggest spending some time there, reading the "stickies".... also go to Amazon and buy all the books you can find.... then work for a while as a 2nd shooter, building up your camera system and becoming an expert at using it under pressure... while learning the business aspects, as well.
There are hordes of "kit camera wedding photogs" out there bottom trolling... I counted 717 ads on my local Craigslist the other day, the vast majority offering cheap wedding packages. I don't recommend you join their ranks.... With their business model, most will be gone back to their day job in a year or so. But each one that goes OBX will be likely be replaced by two or three, each with the same dream, a gleam in their eye, and a new Rebel + 18-55 IS tightly clutched in their hands.
Might want to shoot for a somewhat higher market niche if you expect to have a sustainable, profitable business.