2 -3 months on average
How long does it noarmally take for a players rating to hit the 2000 mark

Hit the 2000 mark at what? Bullet? Blitz? Standard? Chess.com? USCF? FIDE?
The bad news is, 2000 is higher than the vast majority of people make it. The good news is that that alone doesn't mean that you can't. It varies from person to person, depending on how much time and talent they have to dedicate to chess. So don't worry about how long it will take or if you'll even get there. Just focus on enjoying and improving your game and even if you never reach 2000, you can still obtain a respectable rating and have a blast getting it.

For most people it takes never.
For the minority of chess players who hit the mark, it typically takes between 1 year and 50 years.

3 years when you are talented. A bit faster(only 2 years) when you are super talented and/or study chess very much. The standard time for most people is 5 years or more and most of all people will never reach 2000 in their life. And btw. I am talking about Fide ratings(Elo) and not inflated ratings like Uscf.

And btw. I am talking about Fide ratings(Elo) and not inflated ratings like Uscf.
But I am only 2000+ in USCF

3 years when you are talented. A bit faster(only 2 years) when you are super talented and/or study chess very much. The standard time for most people is 5 years or more and most of all people will never reach 2000 in their life. And btw. I am talking about Fide ratings(Elo) and not inflated ratings like Uscf.
Good summary, +1

i am playing for 3 years in the internet. i started around 1100. you can do the math.
Yep, 15 years and you'll be rated 3000.

The bad news is, 2000 is higher than the vast majority of people make it. The good news is that that alone doesn't mean that you can't. It varies from person to person, depending on how much time and talent they have to dedicate to chess.
I would say that 2000 rating doesn't take talent, it takes time and effort. Titled ranks (GM and super-GM) take talent in addition to time and hard work.

I'm sixty, around 1500 here (got as high as 1560..). In ICC, almost 1800. I started playing 35 years ago, never giving chess a structured attention. Yes, lots of funread books and unused software..
And lots of love for the game !
2000 would be nice but..for me impossible. But a nice dream to dream of..
Go, Corinthians !!

always wanted to know.
Years...Talking to people, they say the hardest improvement is to 2000

I'm sixty...
I'll be 58 in a few weeks. I haven't been making much progress at chess... my current rating is a bad joke... but I started a new career last year, in IT (I use to make TV cartoons for kids), and I'm doing amazingly well at it. Who says you can't teach an old dog new tricks?

always wanted to know.
Years...Talking to people, they say the hardest improvement is to 2000
I'm guessing those people are rated near 2000?
Because for people rated 2500, 2000 probably went by so fast they never noticed.

Well, a lot of the players on that level are cheaters.
In a year on this site, I've only encountered two players that I suspected of cheating.
always wanted to know.