In our school this is handeled by the class mothers and not the PTO. The class mothers will send home a notice asking for "X" amount per person and then what they normally do is take the money and buy them a Visa gift card rather than just handing them the cash.
I would suggest you check the IRS website to be certain, but I would think since you are giving it as a gift, your group would not have to withhold taxes. However, I would think the teachers would have to declare it on THEIR income tax forms. How much money are we talking about? That may make a difference too.
Our PTO is collecting non tax deductible money from parents to distribute evenly to our teachers as a Christmas gift rather than each child giving the teachers small gifts. Can the money be distributed without withholding taxes? Does anyone else do anything similiar?