Everytime I slam on the gas my car just sits there after it gets out of first gear. When it finally kicks in it keeps on hesitating. Any one have any ideas on what might be wrong???

I think my 79 has a similar condition.
If it is the same, what someone told me is that it has to do with the vaccum system in the car.

Bascially, it is not a problem so much as something you have to avoid... don't pound the accelerator to the floor, rather steadily and quickly.

Give that a try...if it doesn't help, then I'm wrong.

There could be any number of reasons this is happening.
My 76 had somewhat similar problems. Right now the white princess is running better than it ever has. I got tired of the hesitations and poor performance so I took her to the local engine guru. The biggest problem was the carb but I replaced other potential problems also.
Here's the list... New carb and intake, new fuel pump, rebuild distributor, new plugs and rotor, new fuel lines.
You shouldn't have a hesitation. In my case it was the carb, yours may be different. It can be fixed, its just a matter of finding the problem / problems.. Good luck.

My engine used to run very rough and hesistate, since then I changed to an edelbrock carb and aluminum intake, and ran new vacuum lines elimating some of the "unnecessary" ones. When I took the manifold off the gasket was crumbling and leaking badly loosing vacuum. I did this last year and it is an 80. If yours is the same age ya might want to look at it.

My 79 was also hesitating last year. Not in first gear but when it shifted from first to second. I would get a big hesitation and then powerful acceleration. Really don't know what was causing it, but had the intake manifold replaced this spring with an Edelbrock Performer to match the Edelbrock carb and got a drastic improvement. The guy who rebuilt it also said my timing was seriously retarded, probably from the guy who replaced the carb for me the year before. It was also running too lean, which caused the exhaust to run really hot, thereby causing my right side exhaust manifold to crack. So, after all that: new manifold and gaskets, spark plugs and wires, Dynamax ceramic coated headers, etc. she runs like a charm.

Based on other responses, and my own experiences I would look into replacing the intake manifold or at least the gaskets. Hopefully you have a good mechanic you can trust. Not everyone knows how to work on Vettes.

Hope you get the problem fixed. Let us know how you come out and what you did to solve the problem.