But just this week, Representative Eric Cantor, Republican of Virginia, the House majority leader, reiterated the party’s antitax stance and called for reducing spending by cutting waste and making changes in federal programs. The growth in the so-called entitlement programs, especially for health care, is a main driver behind projections of mounting federal debt as baby boomers age and medical costs rise.

Mr. Obama’s budget was due in February but administration officials said it was delayed by the year-end fiscal negotiations and resulting tax changes. It will arrive on Capitol Hill hours before the president dines on Wednesday evening with a dozen Senate Republicans — his second such parlay in recent weeks.

While the group is likely to also discuss gun-safety and immigration legislation, the timing of Mr. Obama’s budget release is all but certain to make it a prime topic.

Some Senate Republicans have been urging the president to speak out more to Americans about his ideas for reducing the growth of entitlement programs. While the White House posted the offer to Mr. Boehner on its Web site this year, aides previously said that Mr. Obama would not include its provisions in his official budget documents. To do so, some said, would expose him to Democrats’ criticism that he is too quick to compromise and allow Republicans to embrace the proposals for spending cuts, in particular the C.P.I., but ignore those for tax increases.

Neither the president nor senior aides privately hold much hope that Republican leaders — Mr. Boehner and Senator Mitch McConnell of Kentucky, the Senate Republican leader — will compromise. So Mr. Obama’s strategy of reaching out to other Senate Republicans reflects a calculation that enough of them might cut a budget deal with the Democratic Senate majority. If that happens, the reasoning goes, a Senate-passed compromise would put pressure on the House to go along.

According to administration officials, the president’s budget plan would reduce projected annual deficits by $1.8 trillion over 10 years, even with the select spending increases. To offset the initiatives’ cost and avoid adding to deficits, Mr. Obama will propose the tobacco tax increase, a limit of $3 million on how much people can accumulate in tax-preferred savings accounts and repeal of a loophole that allows people to collect both disability and unemployment benefits.

Together with the $2.5 trillion in deficit reductions that Mr. Obama and Congressional Republicans have agreed to since 2010, that would bring the total deficit reduction to more than $4.3 trillion over 10 years by the administration’s computations — just over the goal that both parties have set for stabilizing the growth of the national debt.