There are several problems with Mohler's argument here.
(1) If his system of thinking is correct, we are only 'thinking' what God has preordained us to think, thus if we think we are capable to respond to God's appeal then that is because its the way God made us to think, so why is he acting as if we had something to do with it, or can do something about it? If your going to be a monergist, be a consistent one.
(2) Synergists DO NOT believe, as is asserted here, that we are "smart enough, spiritually sensitive enough, and responsive enough to chose to confess Christ without the prior work of God in our hearts," because we believe the Gospel to BE a prior working of God in our hearts. Why wouldn't Mohler? Maybe what he meant was, "...smart enough, spiritually sensitive enough, and responsive enough to chose to confess Christ after the powerful appeal of the gospel called us to be reconciled." And even still that has yet another problem...
(3) Surrender, brokenness, weakness, poorness of spirit, depending on another, crying out for help, confession, and humility are never seen as boast worthy traits by the world's standard and they do not merit salvation. Mohler seems to think they do both by his use of the word 'enough.' Enough for what? To earn God's favor? To deserve his grace? Does he really think that is what we believe? If so, he is attacking a strawman, because we believe salvation is of grace alone and no one has enough of anything to merit it.