The geography of this does tend to mostly follow "stereotypes" - birth rates in "red states" in the Mountain West and Great Plains and higher than in New England or the West Coast.
But the way this was interpreted during the Bush Years - "Conservatives will win in the end because we have more babies and will outnumber you barren liberals," - turned out to be a fallacy.
This is because nobody in the United States is having enough children to even maintain their numbers, let alone increase them. In 2017,
the only places in the US where fertility rate was above replacement rate were Utah, South Dakota, Guam and American Samoa.
So the story isn't places with high birthrates overtaking places with low birthrates. It's places with absolutely terrible birthrates making up for it with high domestic and foreign migration, and places with only modestly bad birthrates losing population anyway because nobody wants to live there.