Plus que l’infini(e) xxx is per se an exaggeration.

I agree with Greg that taken literally, l’infinie majorité doesn’t make a lot of sense but it is not completely unheard.

I found at least this occurrence in the 1791 Apologie de la constitution française:

It can be put in parallel with the common infime majorité, which means just a little bit more than the majority (50% + epsilon) and thus would mean (100% – epsilon) which is larger than the much more common écrasante majorité (like in a landslide victory).