If I win a sweepstakes is the money taxable?

In the US - winnings of any sort of lottery, gambling, raffle, contest, etc are taxable as ordinary income. You won INCOME from someplace...and that is what income tax is paid on.

Yes, about 20% depending on where you live.

Actually at your marginal rate, which depends on the tax for the State you live in and is on top of the US Federal rate you'll pay. That rate is somewhere between 15% for low income, to about 25% for modest and quickly becoming about 32-35% for higher incomes.

If the sweepstakes is a winning of over $600, they may withhold the tax from the payout, frequently at a 20% rate, albeit what is withheld is not what one actually pays.