I'd bet every nickle I've got (both of 'em) that no US major will ever sponsor expat pilots. They just don't need to; regionals remain an unknown at the moment.
This from UPS addressing sponsorship. I assume they've gotten apps/inquiries from foreign nationals or they'd have no reason to even mention sponsorship in the requirements:
Other information:
• Employer will not sponsor visas for position.
• No company-paid relocation assistance available.
• Must be a U.S. citizen or National of the U. S., an alien lawfully admitted for permanent residence, or an alien authorized to work in the U. S. for this employer.
AviationJobs.Me Flight Crew: B747-400 Non Type Rated First Officers UPS US
And this from Expressjet, not the best regional in the bunch:
"Authorization to work in the United States without sponsorship"
http://www.expressjet.com/careers/pi...ualifications/