President Obama will propose a plan to raise $320 billion over the next 10 years — by raising taxes on America’s wealthiest individuals and biggest financial institutions.

The massive tax proposal, to be announced Tuesday night in the president’s State of the Union address, will include a hike in the capital-gains rate and the elimination of a tax break on inheritances, and would fund some

$235 billion in new tax breaks for the middle class over a decade.

The proposal is expected to be cheered by the Democratic Party’s liberal base.

But while Republican leaders have said they share Obama’s desire to reform the nation’s complicated tax code, the capital-gains and inheritance-tax “reforms” are expected to be nonstarters in the new, GOP-controlled Congress.

As a centerpiece of the plan, the capital-gains rate on couples making more than $500,000 a year would be raised to 28 percent.

In touting the plan Saturday, ­senior administration officials noted that a 28 percent top capital-gains rate would bring it to the level it was under President Ronald Reagan.

But Obama during his presidency has already raised the top capital-gains rate from 15 percent to 23.8 percent — and hiking it further would almost certainly lead to GOP push-back.

The administration also wants to close what it calls the “trust-fund loophole” by requiring ­estates to pay capital-gains taxes on securities at the time they’re inherited.

Administration officials are ­insisting that change would impact only the top 1 percent of income earners, but it’s still ­another likely bone of contention among conservatives.

Most Republicans want to lower the capital-gains tax or eliminate it entirely, and also want to end taxes on estates rather than ­expand them.

Perhaps more palatable to Republicans will be the president’s planned proposal for new fees on the roughly 100 US financial firms with assets of more than $50 billion.

The fee would be similar to one proposed last year by then-House Ways and Means Committee head Rep. Dave Camp (R-Mich.), ­although Camp’s plan was part of a larger proposal to lower the overall corporate income-tax rate.

The new revenue generated by Obama’s plan would be put to use funding a series of measures aimed at aiding middle-class Americans.

One measure would extend tax credits of up to $500 for families in which both parents work and with annual incomes of up to $210,000.

Another measure would expand the child-care tax credit to up to $3,000 for each child under the age of 5. More than 5 million families would benefit from that ­reform, officials said.

Yet another measure would overhaul the education tax system by consolidating six provisions into two. That overhaul would cut taxes for some 8.5 million families, officials said.

Republicans aren’t rattling their sabers on the reforms just yet, despite their anger over the president’s vows to veto party priorities including the Keystone XL oil pipeline, GOP plans for ratcheting back ObamaCare and blocking his executive actions on immigration.

“This can be a moment the president pivots to a positive posture,” new Senate Majority Leader Mitch McConnell has said of the president’s State of the Union speech.