According to Mark 16:17-18, true believers can drink poison and handle snakes with no ill effects:
Some people today believe in faith healers, but I doubt anyone really thinks that believers can drink deadly poison with no consequences. However, these verses are part of what's called the "Longer Ending of Mark". I'll quote from the NIV Study Bible:
So if the Longer Ending of Mark is doubtful, this would tend to eliminate the problem. However, you may occasionally encounter people who want to argue for the Longer Ending being genuine. For such people, the problem is more difficult, though you could still argue that "those who believe" refers only to the early Christian missionaries. I find such an interpretation doubtful though.