If I invited a lady friend to come visit me from the Philippines and I married her while she was here would she be able to remain in the states?
As long as there was no "preconceived intent" (marriage was executed at least 60 days after arrival) or visa fraud involved, & if you are a U.S. citizen, then you can petition her for a "greencard". See: http://www.uscis.gov/green-card/green-card-through-family/green-card-immediate-relative-us-citizen.
I do recommend you speak with an experienced immigration attorney before filing anything, as she could still be denied on other grounds.