Yes, Biden wants to eliminate the stepped-up basis exemption. No, it does not fall within the $12 million per person exemption (but see below for why that doesn’t necessarily matter).
What is stepped-up basis? Under normal circumstances, if you buy something for $100,000 and sell it for $500,000, you pay a tax on the $400,000 gain. But if your parents buy something for $100,000, you inherit it when it’s worth $400,000, and you sell it for $500,000, then you only pay a tax on $100,000 worth of gain. The basis of your tax liability is “stepped up” to the value of the asset when you inherited it (that is, when it was last transferred) rather than the value of the asset when your parents bought it (that is, when it was last purchased).
The stepped-up basis is sometimes considered a tax loophole because it allows people to completely avoid taxes on the majority of an asset’s capital gains by passing it on to their heirs. And to the extent that it is a loophole, it benefits a person more the wealthier they are because (1) it is easier for wealthier people to afford the upfront legal costs of making the necessary arrangements, (2) more of their assets will be subject to the highest rate of capital gains (capital gains can be taxed at 0%, 15%, or 20% depending on the size of the gain), and (3) there are other ways to reduce your tax liability on an inherited home (which is largest single asset that the average person will inherit in their lifetime, and thus the most likely asset to fall within the 20% bracket).
THAT SAID, there are two major caveats to keep in mind. First, the stepped-up basis exemption is the easiest and most flexible way of reducing your tax liability on an inherited home. So anyone who is unaware of or not in a position to take advantage of the other methods will pay more taxes under Biden’s plan as it is currently structured. Second, the economists who advocate eliminating the stepped-up basis exemption (a group which includes both conservative and liberal economists) also advocate for lowering capital gains taxes as part of the change. This is not currently part of Biden’s plan (though it could be an unstated assumption, or it could be that it’s being withheld so that it can be offered as a concession during negotiations).
If whatever legislation that comes out of Biden’s plan includes a reduction in capital gains taxes and some sort of special exemption for inherited homes, then it is likely that the vast majority of Americans would never see a difference in their tax liability (and possibly even a decrease). If that legislation does not include such measures, however, then many Americans will see a difference in their tax liability (specifically, an increase), and it could be reasonably construed as a violation of his promise not to raise taxes on households with incomes under $400,000 per year. It’s hard to see how his plan gets through Congress without these provisions being included, but it’s worth keeping an eye on it.