The Turnbull government has been warned it will face a "massive backlash" from pregnant women if it pushes ahead with a planned crackdown on paid parental leave "double dipping" that could start as early as January.

Labor is calling on the Senate crossbench to block the move, which could affect up to 80,000 new mothers a year.

The government last week introduced proposed legislation to tighten access to the government's paid leave scheme for parents who are also accessing paid leave from their employer.

If passed by Parliament, the change could come into effect as early as January 1, meaning women who are pregnant now could miss out on government benefits.