The funds would pay for initiatives to boost the middle class — such as tax benefits for childcare, college education and retirement for middle class Americans — as the president continues an aggressive run of policy moves likely to shape debate in the 2016 presidential campaign.
The White House said the capital gains and inheritance changes would almost exclusively affect the wealthiest 1 per cent of Americans, and that 80 per cent of the impact would fall on the much narrower 0.1 per cent band, defined as those with annual income of more than $2 million.
But the proposals are unlikely to pass a Congress controlled by Republicans — who say tax rises would slow economic growth — and the details previewed by the White House over the weekend sparked an immediate backlash.
James Ballentine, chief lobbyist at the American Bankers Association, a trade group, said: "This really comes at a difficult time for an industry that is moving the economy forward. To impose a fee, a flat tax, is certainly not warranted, and I hope Congress will reject this idea."
Read MoreObama's approval rating on Wall Street: 17%
The White House said its proposal — a fee of 7 basis points, or 0.07 per cent, on the liabilities of 100 or so financial groups with more than $50bn in assets — would deter banks from taking on excessive leverage and reduce the risk of defaults that could cause catastrophic economic harm.
The five biggest banks by assets are JPMorgan, Bank of America Merrill Lynch, Citigroup, Wells Fargo and Goldman Sachs and the Financial Services Forum, a Wall Street trade group, noted that its members were already reducing risk and leverage and bolstering their capital bases.
More from the FT:
Obama battles to win trade deal authority
Romney shifts stance from failed 2012 bid
Obama and Cameron warn on Iran sanctions
Mr Ballentine said: "This is really another instance of trying to go after an industry which, by their own description, they moved to reform back in 2009."
Grover Norquist, an influential anti-tax campaigner, said the proposals showed that Mr Obama was increasingly aligned with the populists. "This is Obama and the Democratic party going back to the polices of the 1970s, the tax rates and the regulatory explosion," he said. "It tells you that when [the president] told people he had this moderate bone in his body, all that was nonsense."
Dan Pfeiffer, senior adviser to the president, told CBS on Sunday: "The simple proposition [is] that we should ask the wealthy to pay a little more and invest more in the middle class, give the middle class a raise."
Broader tax reform had been seen as one area where Mr Obama could forge a consensus with the Republican-controlled Congress, but Republican aides said the State of the Union proposals did not bode well for co-operation. Orrin Hatch, the Republican chair of the Senate finance committee, said: "The president needs to stop listening to his liberal allies who want to raise taxes at all costs and start working with Congress to fix our broken tax code."