will the stock 3.4 from a cobalt ss/sc fit on our blower shaft of a 2002 bonnie ssei?

That I can't say for sure. But what supporting mods do you have in place to use a 3.4" pulley? A stock engine should not go below a 3.5" pulley. Also, do you have the ability to scan yoru engine for Knock Retard (KR).

yea, i just need to know if it will fit on the shaft correctly.

If no one can answer this I will go in my shop tomorrow and mike a SC shaft and measure the opening of a stock pulley. I just can't do it right now, sorry. There will need to be a tight fit as there is no key. Does this Cobalt use a Eaton M90 supercharger?

no its the stock m62. we looked and it seems that the stock cobalt pulley will fit the shaft. just wanting to make sure.

Your car has a M90. The hole size needs to be a perfect fit. Otherwise it will slip on the shaft. You will need to get very accurate measurements and then compare that to what I come up with here.

Ok, I went and got the measurements.

Shaft on supercharger, M90 .780 inches
Hole on pulley, stock .775 inches

As you can see, this is a very tight tolerance. So as I said, you better be spot on.