Tax commissioner Chris Jordan faces prison time or $5000 in fines after being referred to a powerful Senate committee over his refusal to make public a list of firms banking JobKeeper payments.

The ATO boss could be found in contempt of the Senate after crossbench dealmaker Rex Patrick insisted Mr Jordan hand over the full list of recipients firms with turnover of more than $10 million, part of his push for transparency and paybacks from the $90 billion program.