The Turnbull government has called for a March byelection to replace the High Court hearing of Labor MP David Feeney after the embattled MP told the High Court he did not have any paperwork to prove he was not a British citizen.

Leader of the House Christopher Pyne said Mr Feeney should stop wasting taxpayers money and go straight to the polls in a Batman byelection that Labor fears it could lose to the Greens.

The publicly funded legal bill for the fiasco is expected to spiral to more than $2 million by the time hearings are completed, with taxpayers forking out $130,000 on barristers for each day of the high court case.

"David Feeney has had seven weeks to produce the so-called documents he claims exist proving he renounced his UK citizenship, the fact that he hasn't been able to provide them proves they simply don't exist," Mr Pyne said.