Probably not
If you have any kind of social site, you need moderators. More the users / posts, more the moderators. And good moderators are tough to find. Though you could promote some of your users to moderators... though it will cost.
But I digress, getting a HUGE site going needs a lot more than 1-2k. Have you even seen what an average ppc campaign costs? Forget about development, hosting, management and maintenance. Just promotion cost on a big site would be in the $50k - $250k range.
On-demand hosting would set you back by the 1-2k outlay that you plan. The web is no longer a place for small timers or eureka moments. That day has gone my friend.

Though fortunes will still be made online, returns are fast becoming more a function of the amount you invest.
Now its about cold hard facts. How much does it cost to get the word out to ten million users to start with, assuming that the idea is killer and that word of mouth works for the balance of the web user base (imho 1,000,000,000).
If you believe that you have a killer idea, draw up a business plan and take it to a
relevant incubator (shortlist one or max 2) - patent/ trademark/ copyright the idea before you do though and take along a NDA.
Or beg/borrow from friends and relatives and get it going, professionally. After all, if its going to make pots of money why shouldn't those closest to you benefit? But only do that if you're sure, they wont let you forget it for the rest of your life if you lose their money.
I would recommend spending your 2k on a domain portfolio, promoting and then monetizing them to earn 2x-10x on your investment. Unless of course you prefer a casino to the stock market.
NOTE : The views expressed in this post are just mine, you might or might not agree with them or the gloomy picture I have drawn here for the small timer.