i don't have a rec letter for every sorority...

What they know about you will be limited to the info on your rush registration form. If you are gorgeous and have an unbelievably impressive resume, these houses may notice you. If you are like every other pnm (pretty, good grades, involved, some leadership), you will probably fall through the cracks at these houses and get cut early for not having recs. Just being honest. When we're working our way from 2000+ PNM's down to a pledge class of 150, grades and no recs are the fastest way to narrow down the list.

Forgot to say, even if your registration resume does get you noticed, some houses have national policies that you MUST have a rec to pledge.

You have another week or two to find the recs for the missing houses. Are you sure you exhausted every possible idea to connect with alumnae of these houses???

It depends-- some sororities require a rec to pledge a girl, so if you don't have a bid, then you're kind of screwed for those. Some of them are also competitive enough that you basically have no chance without a rec. at this point, there's nothing else you can do about the chapters that you don't have recs for, so just go in with an open mind, because who knows, you may end up in a chapter that you didn't have a rec for.

Do your best to get a rec, but then don't worry about it. If a group really likes you, they'll get a rec for you.
But honestly, if you're from a big city where there are like dozens of members of a particular sorority, you'll look lazy because you don't have a rec.
I know that's contradictory, but that's how it is.