When venues are open there are also a range of different rules, including about when alcohol can be served and if people are eating.
The bill is due to begin its first reading this evening. National Party leader Christopher Luxon told Newshub this morning he would support the bill, which has strong support from the retail sector.
Baillie said his bill would also look after workers by keeping existing employee protections in respect of Easter Sunday, and extend these protections to Good Friday.
But that bill has been doomed even before its first reading. While Labour had indicated it could treat the bill as a personal vote, Acting Prime Minister Grant Robertson said they were now treating it as a party issue.
"We will be opposing the bill," Robertson said.
"I think there can be a few days in our calendar that focus on spending time with families and not putting pressure on people going out to work."
Act Party leader David Seymour said he was "astonished" at the move.
"I'm astonished labour would whip a conscience vote, especially when on alcohol and religion," Seymour said.
"But that's what they've done."
Seymour said he knew some Labour MPs said they would support it, but didn't know if there would have been enough to pass the bill anyway.
Another private members' bill, those drawn from a ballot, to have its first reading this evening is Labour MP Greg O'Connor's Child Protection (Child Sex Offender Government Agency Registration) (Overseas Travel Reporting) Amendment Bill.
That bill is intended to crack down on registered sex offenders travelling overseas to abuse children.
A bill needs a majority of the 120 MPs to pass. As Labour has a majority only bills it supports can pass.
Parliament has had many similar debates about whether strict Easter trading rules should be relaxed. In 2016 Parliament responded to the debate by giving councils the power to create a policy to allow shops to trade on Easter Sunday.