WASHINGTON — When President Obama releases his proposed annual budget on Tuesday, he will grab his best opportunity of the year to show, in one comprehensive package of hard numbers and precise detail, how he would have the government address what he has called “the defining challenge of our time” — economic inequality.

Many of Mr. Obama’s perennial proposals on education, job training, research and more have hit a Republican wall in Congress, but this year the president is adding one with echoes of Republicans’ own ideas. He will propose expanding a longstanding tax break to better benefit workers who are childless, which the White House estimates will help 13.5 million additional Americans who hold jobs yet remain poor. The current tax break favors low-wage workers with children.

Mr. Obama would offset the costs, $60 billion over 10 years, by ending two tax breaks for some wealthy taxpayers, as a Republican House leader also recently proposed as part of a broader plan to overhaul the tax code. The changes would close loopholes that lower taxes for some self-employed professionals and investment-fund managers.

The White House had recently signaled that Mr. Obama’s budget for the fiscal year that begins Oct. 1 would embody Democratic priorities, shorn of unrequited concessions he made to Republicans last year in hopes of a bipartisan bargain on tax and spending. But by including the new tax-credit proposal and emphasizing its limited Republican pedigree, Mr. Obama is underscoring his struggle to set an agenda that stands a chance to become law, at least in part — in this case, to try to reduce inequality of incomes and economic opportunity.