There are people, like Bernanke, who talk as if electronic dollars are different than paper dollars. These are really both part of base money but for this post let's think of them as two different types of dollars.
Dollars in a bank's reserve account at the Fed are "electronic dollars" and green dollars on paper are "paper dollars". Now the Fed maintains a 1 to 1 peg between these two things. If a bank gives them a paper dollar the Fed will credit them an electronic dollar. If a bank has an electronic dollar it can turn it in and get a paper dollar.
Since there is a 1 to 1 peg between electronic dollars and paper dollars, it is really the banks and their users that determine what fraction of the base money is paper money and what fraction is electronic money. It is not really up to the Fed.
If the Fed makes lots of new electronic dollars, and people still want the same ratio of electronic dollars to paper dollars, it will result in lots of new paper dollars as well. They might not have to print the new paper dollars the same day they made the electronic dollars, but after things equalize they will.
Since the Fed can make both electronic dollars and paper dollars, it can theoretically always maintain the peg between electronic dollars and paper dollars at 1 to 1.
However, imagine that many people holding government bonds no longer roll them over and want to get paid in paper dollars. There could suddenly be $1 trillion of electronic dollars turned in for paper dollars. I am sure the Fed does not have enough $20 and $100 bills around to cover this. It would probably take a long time to print a trillion dollars in $20s or $100s. So what would the Fed do? It would probably make a $1,000 bill and maybe even a $10,000 bill.
In the Caribbean many people won't take a $100 US bill now because the risk of counterfeit is too great. I doubt that a $1,000 bill or $10,000 bill would go over well.