I did my primary training out of a grass strip in a tired 172. We used the shorter 1,900' grass runway frequently, both for takeoff and landing, without much trouble, although I was skinnier back then. (Low field elevation, thankfully.)
Like everyone else said, it depends on DA and weight, but 2,000' is plenty if you have no significant obstacles to clear and the DA is reasonable.
With two big guys in a 172 on a hot day, the 2,500' crosswind runway at my home field is marginal for takeoff, especially with wires and trees near the departure end.
There's only 2,110' available for landing and it's still plenty long for a 172. (Makes life interesting in the Cirrus though.)
Take the performance charts and add 50% (or better yet, 100%) and things should go just fine.