Repealing the $10,000 cap on state and local tax deductions, known as SALT, could be paid for by increased IRS audits, Rep. Josh Gottheimer, D-N.J., says.

Making sure that so-called tax cheats pay their fair share could also help fund parts of President Joe Biden's $2.25 trillion infrastructure plan, he said.

"In a letter that I'll be sending to the Treasury Secretary this week, I believe and I'll argue that we can pay for both by closing loopholes and going after all those tax cheats who don't pay what they should," Gottheimer said during a Monday press event.

More from Invest in You:
Deepak Chopra warns of impending disaster unless people address well-being
How companies can keep women in the workforce
To combat financial illiteracy, education needs to start early in school

The $10,000 cap on state and local tax deductions from former President Donald Trump's 2017 tax law has hit certain states with high costs of living and high taxes the hardest, coinciding with left-leaning areas.

Gottheimer, along with a group of House Democrats and Republicans from high-tax states, recently formed the Bipartisan SALT Caucus to eliminate the cap. The group has said that they won't support any infrastructure plan that doesn't include a repeal of the SALT cap, potentially creating a snag in the package's road to becoming law.

How to pay for Biden's infrastructure plan

The problem is that the SALT cap helps pay for Biden's infrastructure plan, a sweeping package that includes funding for transportation infrastructure, as well as affordable housing, care for the elderly and disabled, better access to broadband and job training.

In the first year that the cap was instated, the federal government brought in $77.4 billion from the measure, according to the nonpartisan Joint Committee on Taxation. If the cap were taken away, it would cost $88.7 billion in 2021 and more in the following years, the committee said.

The White House has thus been hesitant to support a repeal of the SALT cap and tasked those asking to reinstate the full deduction to find a way to pay for it.

Gottheimer's proposal to pay for doing away with the SALT cap targets the tax gap, which IRS Commissioner Chuck Rettig said could be as high as $1 trillion per year in a Senate panel last week. That figure is much higher than the $441 billion per year the IRS estimated was unpaid between 2011 and 2013.

"We need the administration's support and increased investment for enforceability for our current tax laws and help close this massive tax gap," said Gottheimer. "In other words, there is a way to do this by actually going after what people owe already."

Gottheimer has also co-sponsored legislation that would close the tax gap proposed by Representative Ro Khanna, D.-Calif. Khanna estimates his bill would raise $1.2 trillion over a decade by increasing audits on large companies and high earners.

Of course, while reinstating the full SALT deduction is important in high-tax, high cost-of-living states, it wouldn't help most Americans, data shows.

The top 20% of earners would reap more than 96% of the benefits of a SALT repeal, and the top 1% of all earners would see 57% of benefits, according to the Tax Policy Center. The same analysis showed that only 9% of American households would see any benefit from a repeal of the SALT cap.

SIGN UP: Money 101 is an 8-week learning course to financial freedom, delivered weekly to your inbox.

CHECK OUT: How to make money with creative side hustles, from people who earn thousands on sites like Etsy and Twitch via Grow with Acorns+CNBC.

Disclosure: NBCUniversal and Comcast Ventures are investors in Acorns.