With less than a week of tax season to go, plenty of taxpayers are still sorting through the new regulations signed into law by the Tax Cuts and Jobs Act. But middle-class homeowners who live in high-tax areas are finding themselves particularly hard-hit. Many owe thousands this year, rather than the refunds they usually received.

Their problem sits with the new deduction cap on state and local taxes, which the law caps at $10,000. Before 2018, taxpayers were allowed to deduct their total combined state and local taxes from their federal taxes, softening the blow of high property and income taxes in states like New Jersey and California.

The impact is keenly felt by middle-class homeowners who live in towns with high property taxes, which some told CBS MoneyWatch they choose for their great public schools. Getting slammed by higher taxes under the new tax law has prompted some to rethink their plans, even mulling moving after their kids graduate from high school.

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Making it worse, they say, is a perception that the SALT deduction cap is only hitting wealthy families, which they say isn't accurate.

"Every county in my state, but one, had an average SALT tax deduction that was over $10,000. That means average people are suffering," Rep. Bill Pascrell, a Democrat representing New Jersey, said in a House committee meeting last month.

"The rest of the country thinks it's only affecting people who are wealthy and who can afford it, but we know it's not just the case," said Kate Fawcett, who lives with her family in Glen Ridge, New Jersey. "This is just going to wipe us out."

11 million taxpayers hit

Fawcett isn't alone. Almost 11 million taxpayers in high-tax states like New Jersey will lose out on $323 billion in deductions because of the SALT deduction cap, the Treasury Department estimated last month.

About 80 percent of the full SALT deduction had benefited Americans earning more than $100,000 per year, according to the Tax Foundation. But families in high-tax states like New York and New Jersey have a higher cost of living, where $100,000 doesn't stretch as far. For instance, a taxpayer earning $50,000 in Fort Lauderdale, Florida, would need to earn $101,000 to have the equivalent quality of life in Manhattan, according to financial site NerdWallet.

Some filers who have their SALT deductions capped this tax year may see little to no refund this spring but could still benefit from more take-home pay because of lower individual tax rates. But overall, the Tax Cuts and Jobs Act, which was signed into law by President Donald Trump at the end of 2017, isn't viewed favorably by most taxpayers. Only one in four taxpayers say the overhaul made their taxes go down, according to a recent CBS News poll. About one in three say they expect to pay more in taxes.

Among Democrats, fewer than one in seven say they believe they'll come out ahead, while almost half say they believe their taxes will rise this tax filing season. Many of the taxpayers hit by the SALT deduction cap live in high-tax states that tend to vote Democratic, such as California and New York.

Property tax

In Fawcett's case, her family has combined annual property and local taxes of about $27,000. She describes her house as modest, with two bathrooms and three bedrooms, and located on a small piece of property. The new tax law means they are paying $17,000 in taxes they can't deduct from their federal return filed with the Internal Revenue Service.

"Last year we had a refund of about $1,000 from federal," she said. "Our accountant said we definitely will owe $5,000, minimum, but it could be more than that."

While Fawcett said they will have the money on hand to pay the tax bill, she said they are considering refinancing their house to ensure they have money socked away in savings in case of an emergency. In the long-term, she said she has thought about moving once their youngest child graduates from high school.

"It's a huge impact," she said. "It really changed how we think about staying in this town."

Recalculating the real estate math

Some taxpayers said the deduction cap is hurting middle-class families who moved to high-tax areas for good public schools. Others said they were seeking a better quality of life and moved into a more expensive home, only to get walloped by the deduction cap.

"All the exact numbers don't really hit you until you're there," said Ryan Mills, 30, of Vero Beach, Florida, about moving from a $400,000 house to one valued at $1.1 million. He concedes it's "a first world problem," but said owing taxes was "a little disheartening."

As for Fawcett, the New Jersey homeowner, she said she understood the law meant she'd pay more, and that people who live in low-tax states aren't likely to commiserate. "But it was still hard to swallow," she added.

Irina Ivanova contributed reporting.