The United States Note (Greenback) was a pure fiat currency used by Abraham Lincoln to pay for the Civil War and avoid dependence on foreign banks. It has been used a few times since, to help stimulate the economy, but was pulled in 1971.
President Obama can issue Greenbacks today and deposit them in the Treasury's account to pay for daily deficits, including debt service. Only in this way can the deficits provide the expansion of the money supply needed to stimulate the economy.
The alternative of federal borrowing -- the only way deficits are paid currently -- creates no new current, actuated money, the sale of federal debt ("Treasuries") drawing money out of the economy in order to pay federal expenses. Quantitative easing is an ineffective workaround which the Greenback obviates.