The 1916 comment was utterly moronic and Obama's bayonets reply was actually pretty damned correct.
Where are the numbers of ships in 1916 http://www.history.navy.mil/branches/org9-4b.htm#1910
Let's see what's on there ...
3 Monitors ... these are basically US civil war holdovers. By 1916, these were almost half a century out of date. They were utterly useless against any modern navy by the standards of the day. How many obsolete whips does the US currently have? I think some of the battleship haven't been officially decommisioned, so maybe those count?
17 Steel Gunboats ... the fact alone that they felt the need to prefix the name of this class with 'steel' should tell you something. These weren't QUITE obsolete YET but for any operations outside of the US's own territorial waters ... better have your will in order.
25 Auxiliaries ... for the most part, these were SAILING ships. Again, even by the standards of the day, they were obsolete and only good for brown water operations.
11 Gunboats ... If the Steel Gunboats were bad, these were worse. Useful only to scare unarmed civilians.
That's 56 out of the 245 ships that were obsolete (or as good as).
But then again, how much thought does Romney put into anything? He's a good public speaker but his message is somewhat lacking.