If the trait is completely neutral it will double every generation (until saturation is setting in). If the trait is like 10% negative then it will instead increase by a factor of 0.9*2 = 1.8, which is still pretty quick.

Only if it is extremely negative, by more than halving amount of offspring, will it be selected out.

That's in the short term. Presumably, some sort of resistance would evolve in the long term.