We’re not far from that; Canada has already gone that route. They don’t make pennies anymore, and their dollars (and two dollars) are coins only. I see more and more small businesses here dropping the penny already, and as I understand it, it costs more than one cent to make each one.
This is actually a good idea. Both the penny and the nickel actually cost the treasury more than a penny and nickel respectively to mint and issue. Also, given our minimum wage laws, even if a worker were to bill by the minute, the smallest increment would a dime. i.e., if you are paid .10¢/minute, you are only making $6/hour.
Here's what I think we ought to do from a monetary perspective:
The biggest problem with dropping the nickel is that it can cause rounding issues. (i.e., a dime won't divide evenly into a quarter. There used to be half-dimes, but they were not favored in circulation, mostly because of size issues. At the time we had actual constitutional money.)