I think that it is possible for your average person to hit 2000. I myself have done it in over the board chess. It isn't so much talent at our level its more about hard work and putting the time into doing tactics and studying positional chess. Alot of it I think is learned behavior.
Can an average person ever break 2000?

Absolutely. It is common knowledge that the average chess enthusiast will rate about 2000. Anything over about 2300 requires special dedication and training, however.

I think it's an attainable goal for most reasonably intelligent people if it's something that you really want. Then you're more likely to do the studying it would take to reach that level. Obviously some people are naturally gifted in the thought processes required in chess. Anything very far above 2000 seems to be getting into the artistic side where some of us just aren't made of the right stuff, but I could be wrong.
Personally I tend to max out in the 1600's, then find something else I'd rather be doing for several months and slip back down. I've noticed that players ranked 1300-1600 do not seem to have a real wide gap in skill level. It just depends on how strengths and weaknesses match up. For me, players over 1700 are really tough to beat. They just don't make many mistakes to exploit and are very good at exploiting weaknesses in my game.
I think if I were to continue studying and playing and doing a good job of analyzing my games on a daily basis I could get to 2000 in a few years but it's not a big goal of mine so I wouldn't bet on it. I enjoy the tactics trainer so that helps. I try to play against opponents who are better than me which I think is important. A great way to find gaping holes in your game is the Chess Workout on here. I think they are a lot harder than the tactics trainer. If you could solve every one of those positions you'd be on your way to 2000 for sure!

How can an average person break 2000 when 2000 isn't an average rating for players? If you really were a 2000+ rated player you wouldn't be AVERAGE anymore. That's what average means... mediocrity, ordinary, middle. Stop asking ridiculous questions.

yes. everyone can do this with enough deliberate practice. what everyone won't be able to do is become an FM, IM or GM.

Something you might find interesting on this topic of an average person training to master a skill, is this guy Dan who quit his job to attempt to become a professional golfer by training for 10,000 hours. I don't really follow how he's doing but I think he's kind of struggling. He has a website that tracks his progress. http://www.thedanplan.com/
I'm not saying that 2000 in chess equals golfing at a pro level, but it's a pretty interesting topic nonetheless.

So most people tend to agree that most people could get to 2000. Does this apply to speed chess as well? I think less people would be able to accomplish that, but I have limited experience in speed chess so its hard for me to say.

...I don't really follow how he's doing but I think he's kind of struggling. ....
Geez, from nowhere to 6 handicap in 2½ years is kinda impressive.

yes. everyone can do this with enough deliberate practice. what everyone won't be able to do is become an FM, IM or GM.
if everyone can do this then the average rating of all players should be way above 2000 which is silly because the average is 1200.
*facepalm*
Not everyone is putting in the effort. What's being asked is how far above his peers a person with average potential can excel with enough hard work.

Yes. Some can, some can't. To quantify it, I would think that if 100 truly average people tried their best, that over 50 of them would be rated over 2000 in 10 years.

Reaching 2000 OTB is certainly not an impossible task but a demanding one, especially if you start as an adult (then it becomes really difficult).
You basically need to put a lot of time into it and enjoy it.
Chess learning is similar to learning a foreign language, with an added component of fighting spirit.

Yes. Some can, some can't. To quantify it, I would think that if 100 truly average people tried their best, that over 50 of them would be rated over 2000 in 10 years.
I wouldn't be as optimistic as ozzie - but I guess it depends on what "tried their best" means. Anything under 20hrs/week probably wouldn't be enough for most adult players.

How can an average person break 2000 when 2000 isn't an average rating for players? If you really were a 2000+ rated player you wouldn't be AVERAGE anymore. That's what average means... mediocrity, ordinary, middle. Stop asking ridiculous questions.
I love it when someone completely misses the point whilst saying the point he is arguing against is ridiculous. Always worth a chuckle.

Besides playing chess, not thinking chess is a pretty good way to learn more of chess. Take a break, walk outside, get fresh air, hang out with friends and take your mind off the game. And when you get back with a fresh mind, you'll have fresh ideas and different perspectives of the game. Because that's how you win; you can't be restricted to only a couple of ideas, but a multitude of them. Imagination is key. And you'll only improve imagination by having an half-empty, half-full mind, ready to be emptied and filled with ideas.
Your words are the perfect answer for this guy:
Personally I tend to max out in the 1600's, then find something else I'd rather be doing for several months and slip back down. I've noticed that players ranked 1300-1600 do not seem to have a real wide gap in skill level. It just depends on how strengths and weaknesses match up. For me, players over 1700 are really tough to beat. They just don't make many mistakes to exploit and are very good at exploiting weaknesses in my game.
I myself take weeks/months off playing chess, but when I come back it's only a matter of shaking a bit of rust off and then I'm at least at the same level as I was before. No way you're going to fall back. And if in the period you stop playing you keep a bit in touch with strategy and tactics(like reading chess books every once in a while-I mean solving the positions in them, not just skimming), then you will certainly end up a better player. When you stop playing for a while you're not "stressed" anymore about winnig, losing or whatever. And by doing a bit of exercises at this time you are adding new weappons to your arsenal, you are actually gaining more understanding of chess.

...I don't really follow how he's doing but I think he's kind of struggling. ....
Geez, from nowhere to 6 handicap in 2½ years is kinda impressive.
I'm a tough critic right?
I would LOVE to have a 6 handicap! Ok so I was misinformed that he had already trained for 9,000 hours and had yet to score par for a round. He's still got over 6,000 hours left! Web TV show. Sponsors buying him custom top of the line equipment. Professional coaching. Playing golf all day. So you can replace "struggling" from my last comment to "living the life."
How much of chess is art and how much is learned behavior? Just how far can a normal person progress before it becomes something akin to "talent"? Besides playing chess, what is the best way to learn to think chess?