Mosquitos are eating that blood. That means it gets mixed with their digestive fluids. Microorganisms not specifically adapted to that highly destructive environment are quickly destroyed. Malaria and a few other diseases are able to spread that way, but the vast majority (HIV, Ebola, and more) would need some pretty major changes to survive it. Even viruses need time to evolve, and they need a selective pressure to cause the evolution.
The genetic restrictions are even more profound than this. To use a mosquito as a host, a virus needs to replicate in the salivary glands of the mosquito (eg. Dengue, p.falciparum, Yellow fever virus etc.). So, Ebola would have to jump from mammalian specific into insect infection. This wont happen.
Ebola could become more easily transmissible as the air borne Reston Strain exemplifies (fortunately this strain is not human pathogenic) . The epidemic in western Africa strongly suggest that this is not as easy for Ebola as one might have feared, as this didn't happen, but it is possible.
However, there are plenty of other options using insect vectors. Zika virus is a fairly recent human entry and might acquire further mutations increasing its pathogenicity.
Bird flu while not vector borne fits the horror bill quite nicely with high mortality and proven ability to acquire mutations that increases airborne transmission without decreasing (animal) lethality.
All of these viruses (except ebola, because of funeral rites) are fortunately subject to the basic limitations of lethal viruses.
If you kill the host, you stop infecting, so none are doomsday scenarios, but something like the virus in the Söderberg movie Contagion is not ASB.
If you want to go beyond that, you have to think something that is incredibly contagious or kills delayed while still being highly contagious. A human tropic and more dangerous variant of FMDV or maybe measles could be candidates for this (measles can kill by immunosuppression). No known viruses are really obvious for this kind of adaptation, but not every virus is known.