Conflict isn't ours to prevent.
We should protect our citizens, not other countries' citizens.
We will not allow the refugees in.
Public image would only be bad if we let it. If necessary, make laws that bleedinghearts can't speak ill of an America that's only protecting them and theirs. If you still feel bad about it, let people donate charity money to the refugee camps along our borders, individually. Don't force it on the taxpayer.