Usually internships with airlines in the US can only be obtained if you are currently enrolled as a student (grad or undergrad) in a University. The only one that I have seen so far was with Southwest Airlines and it was for the business guys oppossed to flight or ops. I get alot of info still from the university I attended, but like i said. If you are not enrolled at any school, you are not eligible. AND most tend to be un-paid but you get flight benefits or other rewards of sort. My best advice is to research all the airlines you want to work for and check their website. Companies like FedEx and UPS have 1 year co-ops thats typically the longest...unless they offer you a job. but ill say it again, havent seen any that will take graduates. If you're looking to be a pilot for a major here in the US there are no "sponsorships" or things of that sort where you can slide in with no experience and fly jets like in other countries...
Figured i'd try to help...good luck