Even though it's only 3 mil, it would probably work fine, but I agree with Trader that it'll be harder to work with because it'll be easily damaged.
Whatever you do, DON'T use two layers of 3 mil plastic to make a 6 mil vapour barrier. If water ever gets between those two sheets (from a flood, or whatever) it'll never dry out and it'll be a breeding ground for mold.
The building code here in Canada requires 6 mil polyethylene plastic for vapour barrier.
But, the truth is that when companies make this plastic, it's thickness can vary. So, if you buy plastic that claims it's 6 mil, that means that the thinnest area in the roll is guaranteed to be 6 mil or more.
You'd be better off just buying something labeled as "vapour barrier", in which case it's probably about 6 mil on average. The stuff that's guaranteed to be at least 6 mil at it's thinnest point costs a lot more than something that just claims to be "vapour barrier".