Right-wing critics of the new mandates argue they will just make the anti-vaxxers dig in. There is clearly some truth to that. Does that make the mandates a bad bet?
No. Biden is assuming that: the hard core vaccine opponents can only be motivated by sticks at this point; the number of people who will get the vaccine purely as the result of the mandates far exceeds the number who will now never get it for ideological reasons; the economy will improve as a result; and the mandates will have the strong support of the large majority of the population that took the vaccine and resents the irresponsibility of the anti-vaxxers.
My guess is that all of these assumptions are correct.