WASHINGTON — Congress hurtled toward a government shutdown on Tuesday, with Republicans threatening to block a budget deal if it includes financing for Planned Parenthood, as President Obama prepared to join the fight by pushing Republicans to scrap a multibillion-dollar tax advantage for private equity managers.

In a speech on Wednesday, Mr. Obama is expected to call on Republicans to end the tax break and use the funds to pay for spending increases on domestic and national security programs, and he will enlist business leaders to help him make his case.

In a session at the Business Roundtable in Washington, Mr. Obama will seek to shame Republicans who control Congress for failing to strike a deal with Democrats to fund the government’s operations, using the so-called carried-interest provision as an example of what he argues are misplaced priorities, according to White House officials.

The tax break is one that the president has repeatedly proposed eliminating, and it is a favorite bête noire of Democrats condemning income inequality. Its repeal has little chance of passing a divided Congress, but it has gained new political potency in recent days, with two Republican presidential candidates, Donald J. Trump and Jeb Bush, endorsing it.