I'm not sure how I feel about the "vote, vote, vote, vote" to codify Roe part.
Red hats love to hate Biden, so if Biden proactively injects himself into campaign messaging for 2022, citing Roe in particular, that might provide even more energy for people to leave the house and vote Republican, whereas if he would stay out of that part, it might lull the red hats to stay home and hang out on their laurels.
IOW, a continuing entreaty by Biden on Roe might end up motivating as many/more Republicans to vote as/than Democrats.