When you see the mini asteroid hitting earth from space, you see it hitting the ocean and causing this massive wave which would completely cover the earth in water. But, when you see it up close, it's not very big and just covers coastal cities and places.
You klutz! The earth is only 70% water, and an asteroid hitting couldn't change that and magically cover the entire world. As soon as a tsunami hits land, however big it is, it disperses very quickly, quite simply because any wave (including tsunami) is just a surge in water, not actually water moving. This means that as soon as a wave hits land, there isn't any water to surge, so the wave collapses almost as soon as it hits. For a practical demonstration, go to your nearest beach.
Actually, if you had paid attention to what the president was saying, the SMALLER meteor would hit and pretty much destroy the east coast. The LARGER meteor would hit land and cover the earth in DUST, killing all life within a few months.