What was the Bank of United States?

Arthur Rolnick of the Federal Reserve Bank of Minneapolis has argued that in their account of the failure of the Bank of United States: Friedman and Schwartz provide the rationale for the policy that today is known as “too big to fail”—that there are some institutions that are so big that we can’t afford to let them fail because of the systemic impact on the rest of the economy. . . . They suggest that if the Fed had rescued this bank, the Great Depression might only have been a short, albeit severe, recession.
a. What was the Bank of United States? When did it fail? Why did it fail?
b. Why might the Fed’s failure to save the Bank of United States provide a rationale for the policy of “too big to fail”?
c. Are there counterarguments to Rolnick’s view?