The two hold outs against passing the "Build Back Better" bill are standing in the way of the Democrats holding Congress just over a year from now. While Congress, and Democrats in particular appear incapable of getting any legislation passed, Biden's poll numbers are tanking.
Oddly, that may give Biden some leverage. He has only to convince Manchin and Sinema will likely follow suit - she won't want to be the one person to have sunk the Democrats entire post-Trump agenda.
So what will it take to get Manchin on board? How about threatening to primary him from the left? If he sticks to his guns the Senate is lost anyway, replacing him with a progressive won't make any different to the Dem's control of the Senate. But if he likes his job, and I suspect he does, he'll reach a compromise pretty quickly.