Cleft lip surgery is a cake walk... oh wait.. maybe not
I think it's more terrifying and trying on the parents.
Seriously, they can do wonders these days. Beware that surgery is normally done in stages, and you could have 3+ surgeries even for a minor cleft repair. Surgery should be covered by your insurance, as it's not considered a purely cosmetic surgery.
However, as mentioned, you may want to have a full medical workup, as the developmental timeframe that is affected at the same time as the lip/pallete can also affect several other developmental issues.