might have had some dead students on its hands

22:40 Jul 5, 2007 

As I see the phrase being used (here and elsewhere), it means that the administration would have to respond to/deal with the situation (i.e., the death of US students and related public opinion). It means if the administration did not react, i.e., send in troops to rescue US medical students on the island, the Reagan Administration may have had to deal with the media fall-out regarding the (seemingly preventable) death of US students at the hands of the Grenadian military (which had just taken control of the country by murdering the leader of Grenada's ruling Central Committee). Another example of this phrase (outside of this context) might be: A company executive, in reference to the improper behavior of one his managers, might say "we've got to be careful with this one, or we'll have a mutiny on our hands" (meaning if the management fails to deal effectively with the situation, the employees will create problems for the firm).