With a $1.9 trillion stimulus plan now under his belt, President Joe Biden and his administration are reportedly eyeing several tax hikes to pay for a significant new infrastructure bill and help coral the ballooning U.S. deficit.

But getting tax hikes through even to support badly needed infrastructure investments will be a Herculean challenge, argues Stifel chief Washington policy strategist Brian Gardner.

"The politics of a tax bill are likely to be more challenging than the politics of passing an emergency spending bill. Most lawmakers like spending money and being seen as caring and empathetic during a health crisis. However, voting for a tax bill is not as popular since it could include hard choices for key industries and political supporters back home," Gardner says. "Given Democrats’ razor thin majorities in both the House and Senate, any dissension could be fatal to the bill."

That doesn't mean impossible, however.

Gardner lists several tax hikes that Congress and the Biden administration may pass in the currently polarized political climate. They include:

1. Raising the corporate income tax rate to 28% from 21%.

2. Doubling the global intangible low-taxed income rate to 21% from 10.5%.

3. Lifting the top tax rate to 39.6% from 37% for individuals making over $400,000.

4. Taxing capital gains as ordinary income (at a top tax rate of 39.6%) for those earning more than $1 million a year.

5. Hiking the estate tax rate to 45% from 40% for assets worth more than $1 million.

Interestingly, the market appears to be betting tax hikes of any kind are unlikely to happen or that they will happen so far off into the distance that riding optimism on the pandemic recovery makes better sense.

The Dow Jones Industrial Average is up 7.2% on the year, while the S&P 500 has gained 5%. Both major indices continue to hover around record highs. But pros contend that tax hikes could pose a problem to the bullish sentiment on Wall Street.

For his part, Gardner warns hiking the capital gains tax alone could be a headwind to the stock market. Meanwhile, an increase in corporate taxes could take a bite out of corporate America's profits and the multiples stocks are able to fetch.

Recall then 2020 presidential candidate Biden put forth reversing half of former President Donald Trump’s signature tax cuts, lifting the statutory rate to 28%. Investment bank Credit Suisse estimated this change in taxes would increase the effective rate by 4% to 5%, and slash $9 off estimated S&P 500 earnings per share. Goldman Sachs projected that Biden’s tax plan would lead it to reduce its 2021 earnings estimate by 12%.