Physics problem:

Assume of a wave of water 1 meter wide, 3 meters tall, and which hits at least 80% of the coastline of the gulf of mexico. Compute the gravitational potential energy in this wave. Now compare to the energy of a nuke.

(I haven't bothered to do this calculation. But last time I did it, when dispelling conspiracy theories about the last tsunami, it was several orders of magnitude too small.)

It would depend on how far down the bomb was placed. There are a lot of nuclear test craters in Nevada, in fact there's a museum in Las Vegas about it which is very interesting. But most of those craters were from explosions only hundreds of feet deep (back then the environmental risks of nuclear testing were not as widely appreciated).

This image from FAS suggests that below 1000' the surface disturbance and resulting water displacement would be minimal: http://www.fas.org/faspir/2001/v54n1/sm_crater_depth.gif

Some nuclear weapons had relatively small yields - as low as 10 tons of TNT:

http://en.wikipedia.org/wiki/Special_Atomic_Demolition_Munit...