National Australian Bank chief executive Andrew Thorburn and chairman Ken Henry will fight for their jobs amid growing political pressure, insisting the bank has learnt from its mistakes and they can fix its culture following the royal commission.

Prime Minister Scott Morrison and Opposition Leader Bill Shorten turned up the heat on the pair, who Commissioner Kenneth Hayne said had left him unconvinced "that NAB is willing to accept the necessary responsibility for deciding, for itself, what is the right thing to do."