The "last statement"? This would require that there exists a highest natural number. That seems like it would be a weirder occurrence than the mostly harmless Yablo's paradox.
Although I suppose we can always choose to work in "the natural numbers mod N", for some value of N, which is one way to banish "infinity".
There is no need for ridiculously large numbers. There is always the last statement in a row and this way and only this way, no Yablo paradox arises.
Graham Priest discusses The Liar's Paradox for a NY Times blog. It seems that one way of solving the Liar's Paradox is defining dialethei, a true contradiction. Less Wrong, can you do what modern philosophers have failed to do and solve or successfully dissolve the Liar's Paradox? This doesn't seem nearly as hard as solving free will.
This post is a practice problem for what may become a sequence on unsolved problems in philosophy.