I agree with Don Marco. Tessio didn't want to become don, he just didn't think Michael could beat Barzini and wanted to be on the winning side.

I have a feeling even if Tessio did succeed, he would get whacked later on. After all, he did betray his family.. who's to say he wouldn't betray Barzini later on down the road? Barzini could (and probably would, given his attitude and actions) use that as an excuse to have Tessio killed right after consolidating his power.