See I don't agree with this kind of thinking. You win votes by doing things, not by not doing things. Biden is letting himself be hamstrung by concerns about "los[ing] a bunch of Democratic support."
All it would take to turn Manchin into a reliable ally is a little J. Edgar Hoover style blackmail--there's no way the dude has a skeleton-free closet. And taking SCOTUS, by whatever means, would do a lot to win Dems over. Then force through statehood for DC and Puerto Rico and/or Guam, and you've got a solid, long-term Dem majority in the Senate. Power does not flow from a 236-year-old piece of fucking paper, and I'm sick of political discussions that continue to ignore that, as if that damn piece of paper is somehow going to maintain stability in this country over the next decade. I'm sick of Democrats being too afraid to use strongarm tactics like McConnell did, proving again and again that they don't really care about their supposedly preferred policy outcomes at all. Yes, there are consequences for trying and failing, but there are also consequences for not trying, and thus failing by default.