It's about 1,000 miles from US mainland naval bases; That's maybe 48 hours for a warship. The Navy and Marine Corps are in the habit of providing a rapid response to unexpected events - they would be pretty useless as a defensive force otherwise - but a hurricane isn't unexpected; it was known at least a week in advance that it would likely cause severe damage. So the limiting factor in response time is just the time needed to move from holding positions outside the area of dangerous weather and sea conditions to the areas that needed help.
Any modern navy could do it. The US Navy are not that much less effective than the rest of the world, surely?
Bear in mind that the benchmark here is a one week response time. Most of which was, in the case of Louisiana, also due to needless prevarication by the man with the authority to say 'Go!'
The POTUS could easily, and at almost no marginal cost, have instituted a massive military recovery and assistance operation, which could have started within at most three or four days of his giving the order. He chose not to.
Warships don't normally sit around at naval bases when they're in shape to be deployed. Thus the distance to naval bases means very little.