Billy; Genesis 7:2 actually says 7 pairs of 'clean' animals and a single pair of 'unclean' animals.
Now let me play Devil's advocate:
You may be acquainted with the "baramin"(Hebrew for kind) theory of creationists which states that there is a certain, limited degree of variation in the genepool allowing, for example, the felines in our present day to have descended from one "Cat Kind". This amounts to an acceptance of microevolution (and I'm surprised to have heard that very word from Creationists) and also substantially reduces the number of representative animals in the ark. According to Creationists baramins are roughly correspondent to the scientific classification of Genus or Family.
As far as not having time to evolve or speciate that is most probably true taking a 4,000 year time span. However, Sociobiologists like Edward Wilson have stated that if the conditions are right, substantial evolution is possible, within 50 generations. Whether that is sufficient time for Lions, Cougars, Hyenas and your pet cat to vary from the original 'Baramin' or 'Kind' I do not know. Therefore the only way to dispute these arguments is to do some pretty heavy duty math and calculations of migratory patterns etc that no one without a University level of education would be able to understand.
It would also take a very patient soul, minus the University degree, to calculate the square footage of the ark and try to stuff 7 pairs of clean and 1 pair of unclean 'kinds' ("baramin"). It was a pretty large Ark though my intuition tells me it was not big enough.
What we are left with is an intuitive feeling that there is something wrong with the whole story but beware, a smart Creationist can talk circles around us especially if he takes his stuff seriously. There are of course counter arguments against them but a few of them are immune to the "Noah's Ark can't fit them all" debate. That is why we would have to calculate square footage divide by the amount that an inactive animal would need and then compare that number to what exists on earth today and existed yesteryear on the Genus or Family level.
Saying that we need to do more homework should not discourage us or be taken as a sign of ignorance or weakness on the part of evolutionists. Creationists are simply sloppy to say the least. There are a plethora of fact based arguments at our disposal.
For anyone who is interested in the subject I highly recommend the book Science and Earth History by Arthur Strahler. It is devoted to responding to virtually every Creationist claim and with five hundred large fine print pages of material it is very much worth the price.