Ideally, it wouldn't be a case where one country shoulders the burden. If there are any justifications at all for multinational cooperation, this would probably be an easy sell.
We already devote a massive amount of funding to foreign aid -- about $48 billion in economic and military assistance in 2012 according to Wikipedia (http://en.wikipedia.org/wiki/United_States_foreign_aid). We sent about $13 billion to Afghanistan and Pakistan alone in 2012, according to nationalpriorities.org. This is a pretty good match for private-sector pharmaceutical R&D expenditures, about $51 billion in 2013 according to one industry lobbyist (www.phrma.org).