What does “(Mitt Romney) wells up” mean?
Solution 1:
In the article it is not emboldened in the way you have shown it. It simply means he gets emotional to the point where he may appear to have tears in his eyes. As someone who has had experience of Mormons, this is not unusual. The religion encourages and facilitates an emotional delivery of the message by the way people are urged to 'bear testimony' to its truthfulness. They will refer to such as a 'spiritual experience'.