This number has been verified legit, as the federal agency Centers for Disease Control is doing a survey on how many children are vaccinated. If they leave a voicemail the callback number is 1-877-220-4805. I called today (a Sunday) and there was a live person answering. I told him yes I am older than 18 and I don't have kids, and he said thank you that's all the questions I have.
PS. there still may be scam artists trying to spoof this number, even though they don't work for the government. Be careful anyway.