The first quote by Hoover shows a great example of a fixed mindset. He see's that he has tried as hard as he can given the available resources, that there is nothing more to do than watch the situation play out.
The second quote by Franklin D. Roosevelt Is an example of a growth mindset. He decides to continue with what he started. There are no current options, so he will 'tie a knot' as in keep himself involved. He will hold on to hope and monitor the situation.