One possible answer in IMHO would be to combine some of the alternatives already presented here:
Heater system distribution + working area scans
Make your gigantic city be located on a frozen planet or any other place that is cold for the whole year.
Government supplies hot air/steam to all houses to keep inhabitants alive against the cold. Drug is pumped in the ventilation system's central distributor.
Those who work for the government get the antidote everyday on the DNA SCAN at the door to the building where their workplace is.
I really liked the idea of distributing by air or some other central system, you would only need a small crew to insert the drug at the distributor.
Whoever suggested the DNA scans, +1 to you. Gattaca all the way.
Rejuvenation Drug
The government offers a drug that keeps people young and healthy for an unknown life extension period. It really works but you get addicted as a side effect. Sure Mr Jones died after living some 275 years, but what could you expect? He lived well for that much long.
Perhaps the withdrawal only kills the person who took the drug after some period of 6-12 months without the drug. The person would start getting old again, and I really think it would be tempted to take the drug again.
Whenever the government wants someone to "fade" (that is how they call it now,) they administer a drug that cancels the effect of new doses, so the person dies even while taking the drug... poor man, his time hashad come at last.