If President Joe Biden indeed proposes almost doubling the capital gains tax rate for wealthy individuals, to 39.6 percent, investment advisers will encourage many of their clients to sell any assets they're thinking of selling as fast as possible, before the tax change goes into effect, according to Treasury & Risk sister publication ThinkAdvisor. A few of them stressed that their wealthiest clients won't be the only ones hurt by an increased tax rate—many middle-class investors will feel the impact as well.

Biden is considering the capital gains tax increase to help fund his social spending plans, according to people familiar with the proposal. For those earning $1 million or more, Bloomberg reported, "the new top rate, coupled with an existing surtax on investment income, means that federal tax rates for wealthy investors could be as high as 43.4 percent."

The increase stands to affect "a lot more people than people realize," according to Jeffrey Levine, chief planning officer at Buckingham Wealth Partners. "It's not the clients that make a million dollars or more every year that you need to be worried about," he explained to ThinkAdvisor in a phone interview on Friday. "It's the people who might have a million dollars or more in any one year," a group that includes business owners who sell their business or anybody else with a large asset they may sell or buy, such as families involved in the sale of a home, he said. (Home sales are exempt from capital gains taxes under certain conditions.)