http://thehill.com/homenews/campaign/196920-convention-wipeoutAs that story notes, the federal government currently covers ~23% of the costs of the conventions. Eliminating that leaves a funding hole that they'd have to make up from more private donations.
*However*, there's been talk in recent years of scaling back the conventions somewhat, possibly even going from four days to three days, since the networks cover them less than they used to anyway. This might create the impetus for that. Could then also play into the question of which cities are going to host the conventions in 2016.