Let's look at your idea from a realistic standpoint shall we? There are 138 million taxpayers in the United States. Let's assume for this argument that 100% of them decide to participate in your little scheme to "pay down the debt". That comes out to a grand total of $7.2 billion dollars a year. That is before you take out any winnings and of course the gobblement has to pay a bunch of people six figure salaries to administer this little program. And they have to have TV time to announce the "big winners".
But, lets say in this little fantasy land that 100% of the $1 a week from taxpayers goes right to the debt. The debt is $16,000,000,000,0000 (that's $16 trillion in case the zeros confused you)
So $16,000,000,000,000/$7,176,000,000 = wait for it
wait for it...............................
wait for it...............................
2,229.6 years
That's right bubby. Your little "scheme" that I am sure you think is sheer brilliance would take almost two thousand and thirty years to pay off the debt. And that is assuming that every taxpayer participates and that every dime goes to paying down the debt. Assumptions any sentient being knows not to be the case. Hell, lets assume the debt doesn't grow any more from here.
Now I know you will be all butt hurt because I poured water all over what I am sure you think is a brilliant idea that should be brought to the floor of the Congress. But, unlike you low information voters, the rest of us have to live in Realville.