If there is a passenger who's allergic to cats, though, what happens next is up to the flight crew. If the other passenger will be fine as long as your cat is not in their immediate vicinity, you should offer to move to another seat (even if it means you're stuck in the middle seat of the last row on the plane). But if someone on the plane has a truly severe cat allergy, it's possible that the pilot will not let your cat fly in the cabin at all. You might have to choose between putting her in the cargo hold or taking a different flight. Actually, depending on the temperature outside, the cargo hold might not even be an option. If it's too hot or cold for pets to fly in the cargo hold, you'll just get reticketed.
I know that would be incredibly inconvenient for you ... but you have to look at it from the airline's perspective. It's a heck of a lot more inconvenient (not to mention dangerous) if the pilot has to make an emergency landing because someone went into anaphylactic shock.
If you're really worried you'll get taken off the plane and not make it to Denver in time, though, you should consider driving rather than flying. It's a long drive, to be sure, but you'd have much more control over your arrival date.
Lesley Carlin has been writing about travel and etiquette professionally for more than 10 years. As one of the Etiquette Grrls, she is the co-author of "Things You Need to Be Told," and, "More Things You Need to Be Told" (Berkley). Have a travel etiquette question of your own? E-mail Lesley at firstname.lastname@example.org.