The proposal includes some elements that have previously drawn support from both Republicans and Democrats, including education and retirement savings proposals and the secondary earner credit. A tax on large banks was part of a plan proposed last year by former Representative Dave Camp, a Republican from Michigan who retired as chairman of the Ways and Means Committee.

Mr. Obama’s advisers characterized the plan as the next phase in the president’s economic message, which he has been promoting over the past two weeks with trips highlighting the nation’s financial rebound. During the tour, Mr. Obama has pitched a range of initiatives to help the middle class, including free community college and paid leave. The bulk of the financing for the plan — $210 billion — would come from a capital-gains tax hike and a change in the way the tax code treats the appreciated value of inherited assets. Under the proposal, inherited assets would be taxed according to their value when they were purchased. That means the capital gains on those assets during a person’s lifetime, now shielded from taxation, would be subject to tax at the time of the bequest.

The proposal, which does not apply to charitable gifts, would fall almost entirely on the top 1 percent of taxpayers, administration officials said. It would apply to capital gains of $200,000 or more per couple, with an additional $500,000 exemption for personal residences.

The remaining $110 billion to pay for Mr. Obama’s new tax proposals would be generated by a fee imposed on the largest and most highly leveraged financial firms. That proposal, administration officials said, was designed to make “risky activity” more costly for the roughly 100 such companies in the nation with assets more than $50 billion. Those companies would be assessed a fee based on the amount of debt they hold.

White House officials estimated that the new $500 “second-earner” tax credit would benefit 24 million households. The maximum credit would go to those earning up to $120,000, and some credit would be available to those earning up to $210,000.

Mr. Obama also wants to triple the child care tax credit, now an average of $550, and make it easier for middle-income earners to qualify, offering up to $3,000 for each child under age 5. White House officials said the plan would eliminate existing tax-advantaged flexible spending accounts for child care and reinvest those resources in the tax credit.

In addition, the president is proposing to streamline a jumble of educational tax credits and give students up to $2,500 annually toward earning a college degree. Students who attend school less than half the time would also qualify for the first time, and more of the credit, $1,500, would be available regardless of whether an individual owed any taxes.