Paper money has no special significance. There is no difference between paper money and what you are calling ‘electronic debt’, no more difference than there is between paper money and the dollar balances credited to your bank account.
Paper money has always been just a small fraction of the dollars in circulation. The vast majority has always been in the form of accounting entries on bank ledgers.
Under the gold standard there was a distinction made between ‘money’ (also known as ‘specie’) and ‘credit money’ (aka ‘bank money’); but paper currency could represent either, depending on whether the paper currency was a gold note, a US Note, or some other note issue.
When the electronic debt bubble implodes, (and physical history says it must), paper debt notes will be used by some who lack any alternative. That will work for awhile, as others have stated. Eventually producers will stop taking the paper notes and will demand real money (gold, silver eagles, nickels, old pennies, etc..). The long term US affects of the electronic debt implosion can be seen over the short term in Greece right now. Power companies will soon be failing. Prisons cannot feed their inmates. What we need to be doing is finding alternatives to the paper debt notes. The states should be taking control of these issues, since the feds have failed miserably.