Lotteries have been used by governments for fund-raising since colonial days. A national lottery which offered prizes only available through the federal government could make a proportionally large dent in the federal deficit at a fairly low cost.
For example, prizes could include things like:
* A one year exemption from (or refund of) federal taxes paid (income, payroll, Social Security, gasoline, etc.)
* One-on-one consultation/counseling with experts from government agencies (financial, HHS, Veterans Affairs, Education, etc.)
* A lifetime pass to the National Parks and Monuments
* No-fee application to TSA programs like NEXUS, Sentri, or FLUX.
Lottery ticket prices would vary according to the value of the prize (would you pay $100 for a chance to visit the Space Station?)