Rick,
First, I agree with Devin about the possibility of a vacuum leak and/or a gasket problem (the gasket at the base of the carburetor needs to be there and needs to be orientated correctly to a hole in the base of the carb).
It is odd that Rockauto.com does not show a carburetor for a 1961 235 Biscayne but shows a one-barrel Rochester for a
1961 235 Bel Air. Nonetheless, the 1-barrel Rochester should work satisfactorily on any 235 that it can be bolted onto (as long as it is equipped with a properly working manual or automatic choke mechanism).
Tim
