Yes, but they don't need to PAY us anything. Medicine functions as a trust and they know that, since they collude to make sure a fired resident has few if any chances to become a practicing physician, residents don't have any other options other than to finish, no matter how crappy the conditions. The only reason they pay us anything at all is because it doesn't cost them anything. the DME portion of GME funding is a 1:1 reimbursement for what they pay you. They can't even pocket the money and refuse to pay it out, since the reimbursement matches the disbursed salary. So they shrug their shoulders, pay residents a living wage, and tell us how generous the hospital is.
If GME funding ever goes away entirely resident salaries will drop to zero overnight. The number of slots won't necessarily decrease, as other have pointed out we're extremely cheap labor, but residency could very easily become free labor. Or even a tuition paying educational experience, like medical school. This is not something to root for.
BTW all I'm seeing at this link is what I've read before: Medicare is making cuts, and GME is part of medicare. There's no guidance yet as to what gets cut. So GME is either part of the sequester... or not.