Went to start my 1999 Tahoe (~87,000 miles) in the morning and it just turns over and over. Was told that is is most likely the fuel pump.

I am in the process of taking the fuel tank off to get to the pump. Do I need to remove the drive shaft in order to get the tank out?

What other things should I possibly look at?

I usually remove the driveshaft on those models to remove the tanks (gives you a little more room to work)
Be careful with the fuel lines, try not to kink them.

I am not 100% sure that it is the fuel pump. Do you know of any other things to look into before I blow ~$400 on a new fuel pump? I have heard that there is a fuel relay switch somewhere.

Seems funny to me that the fuel pump would just stop without any warning at all.

I'd replace the fuel relay first, as well as the fuel filter. Together they'll be less than $50 and can be done by you. I'm not sure where the relay is, though, so you'll need to do some more research for that one. I don't know that I'd rip my gas tank out, though... that one would be something I'd leave to the mechanic.

Before you replace anything, lets do a little diagnostics first.
Remove the wiring connector from the top of the tank. With a test light. touch the connector at the gray wire. Have someone attempt to start the engine. If the light comes on, then all the wiring and control circuits are good and it needs a pump.
Check the ECM-B fuse, if it is blown, then replace the pump.

Fuel pump is an electrical/mechanical part and will fail with no warning