Essentially Congress is only allowed to lay "direct" taxes on income and a wealth tax is probably income.
The relevant parts of the constituion which states “No Capitation, or other direct, Tax shall be laid, unless in Proportion to the Census." The 16th Amendment then allows congress “to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.”
So the question becomes if "wealth" counts as "income." In "Eisner v. Macomber" the Supreme Court ruled that Congress can't tax stock splits, which suggests that wealth can't be taxed as income. Knowlton v Moore was (perhaps unwittingly) cited by the (mostly liberal) majority in the "National Federation" case asserting that Health Care Reform is legal.
Left of center commentators argue that because estate taxes were found constitutional that a wealth tax that overrides Eisner. But I don't find that compelling, the case treats an Estate Tax as an income tax on the inheritors.
The other argument by left of center commentators is that Congress does "mark-to-market" taxes on future traders (https://irc.bloombergtax.com/public/uscode/doc/irc/section_1256). I don't know if that was challenged in court though. And even then
I hope a wealth tax is never attempted. But if it is, it'll be interesting to see how Kagen responds with all her emphasis on "stare decisis." To me, the idea that a wealth tax is an income tax is crazy, why do we have separate words for the two terms. And if a wealth tax isn't a direct tax what is?
I guess congress can achieve something similar to a wealth tax by having an over 100% income tax. But I suspect that framing the issue would be less popular than a wealth tax. And there's a chance that the court will rule that as a de facto wealth tax.
For left-of-center commentators see https://www.bloomberg.com/opinion/articles/2019-01-30/elizabeth-warren-s-wealth-tax-is-probably-constitutional and http://nymag.com/intelligencer/2019/02/constitutional-concerns-are-a-major-risk-for-a-wealth-tax.html