It is logically possible that there is no continuous series of viable genomes leading from one type of organism to another,
i'm rather certain that it is not. it would require one of the organisms to be made of wholely different stuff. as it stands, finches and lizards have mostly the same genomes.
my post is made of the same letters as yours. theoretically, i could vary your post into mine, step by step, by adding or changing a letter every step. it might take a REALLY long time, but it wouldn't be impossible.
אָרַח