The Turnbull government will face overwhelming opposition from voters in key Liberal and Nationals seats if it supports the move to cut Sunday penalty rates.

With Labor and the union movement working hard to persuade voters that Prime Minister Malcolm Turnbull favours cutting Sunday pay for retail and hospitality workers, exclusive ReachTEL polling conducted for the left-leaning Australia Institute shows the move will face strong opposition from electors in key Coalition seats.

"The government has no plans to change penalty rates": Employment Minister Michaelia Cash. Credit:Graham Tidy

Polling across the federal electorates of Warringah, held by former prime minister Tony Abbott, Dickson, held by Immigration Minister Peter Dutton, New England, held by the Nationals' deputy Barnaby Joyce, and the NSW seat of Page on December 17 found between 65 per cent and 79 per cent of people in those electorates want Sunday penalty rates in the retail industry either kept the same or increased.

In Warringah, 51.1 per cent of electors want Sunday rates for retail workers to stay the same and 13.7 per cent want them increased.