High housing costs and a lack of personal savings are cited by the charity as reasons for this.
The online survey by pollsters YouGov in July questioned 1,581 people in working families with children.
"Strong protections" are in place for "those who fall on difficult times," a government spokesman commented.
The spokesman said: "We are introducing the National Living Wage, increasing the personal tax allowance and giving the next generation choice and flexibility in their savings, including the Help to Save scheme for people on low incomes.
"We are continuing to spend around £90 billion a year on working age benefits to ensure a strong safety net for the most vulnerable.
"And for those who do fall on difficult times, there are strong protections in place to guard against the threat of homelessness, and ensure we don't return to the bad old days when homelessness in England was nearly double what it is today."
The online YouGov survey questioned 8,381 adults, including 1,581 members of working families with children.
It concluded that 37% (585) of such families would be unable to cover their housing costs for more than one month with no job, while 23% (364) said they would be unable to pay their housing costs at all.
Some 48% (759) of families in the survey named the cost of housing as the biggest drain on their budget, the charity reported.
"These figures are a stark reminder that sky-high housing costs are leaving millions of working families stretched to breaking point, and barely scraping by from one pay cheque to the next," Shelter chief executive Campbell Robb said.
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Mr Robb said the government had a "real chance to show working families they're on their side, by protecting and improving our welfare safety net".
A single mother of two children, named only as Lou, told researchers that although she was working full-time as a complex needs carer, and has moved into a small flat, she still finds keeping up with the rent every month a struggle.
She said: "I'm working hard, but it still makes me feel like a failure. I recently changed jobs and hit a rough patch when I thought I wouldn't be able to pay the rent.
"An employer had given me some work and didn't tell me that my hours wouldn't be guaranteed, I lost a chunk of my income all of a sudden, and very nearly lost my home. It was really scary.
"There's never a cushion. You'd think if you were working you'd be able to save a little bit every month, but it's just not a possibility when just paying for the basics is so expensive."
One in three families in England could not pay their rent or mortgage for more than a month if they lost their job, a study for the charity Shelter suggests.