May
According to a recent Applied and Environmental Microbiology paper, influenza viruses are able to survive on banknotes. Lookie, bar graphs:

(from the paper) Duration of infectiousness according to the size of the initial inoculum and the presence or absence of mucus. Influenza A/Moscow/10/99 (H3N2) virus was deposited in triplicate on banknotes at the following concentrations, each in the presence (H3m) or absence (H3) of respiratory mucus: (A) 8.9 x 10e5 TCID50/ml; (B) 4.4 x 10e5 TCID50/ml; (C) 2.2 x 10e5 TCID50/ml; (D) 1.1 x 10e5 TCID50/ml. (E) Similarly, influenza B/Hong Kong/335/2001 virus was deposited at a concentration of 3.2 x 10e3 TCID50/ml in the presence (Bm) or absence (B) of respiratory mucus.
Basically, if the influenza virus is in snot when it hits the bill, it will survive for 24 hours or longer. The authors conclude:
We showed that infectious virus can survive for several days on banknotes. This requires a relatively large inoculum and the presence of a protective matrix, such as respiratory mucus. Pandemic events depend on the presence of sufficient quantities of virus with pandemic properties, as well as suitable vehicles for its transmission, including environmental vectors, such as banknotes. The results of our study show that influenza virus stability is not the sole determining factor in a pandemic. As hundreds of billions of banknotes are probably exchanged every day worldwide, infection from hands contaminated with virus picked up from virus-contaminated banknotes cannot be totally ignored. Given the unexpected stability of influenza virus in this nonbiological environment, our current understanding of the conditions favoring influenza virus survival needs to be revised, particularly in the context of pandemic preparedness.
At least with this metric (and only this metric), the euro is probably doing as poorly as the dollar.