But Mr. Trump, in a dogged effort to fulfill his campaign promises, has turned that logic on its head in the budget outline he is expected to present to Congress this week. That blueprint would make good on his promise to increase spending on the military and law enforcement by $100 billion over the next 18 months. And it would extract all of the savings he can from the one part of the budget already most squeezed, domestic discretionary spending, potentially decimating programs in education, poverty alleviation, science and health.

“For Paul Ryan, this seems to be the opportunity he has been waiting for and working for for years,” said Douglas Elmendorf, the recently departed director of the Congressional Budget Office and current dean of Harvard’s John F. Kennedy School of Government. “But Paul Ryan’s budget plans with cuts to Social Security and Medicare are not that popular with most voters, and what helped elect Donald Trump was the promise not to cut benefits and programs, and that is an unresolved tension.”

None of this should be a real surprise: Mr. Trump repeatedly said during the campaign that Republican promises to transform Medicare, and slash entitlement spending, were the reason the party lost the White House in 2012, helpfully name-checking Mr. Ryan, who sat at the bottom of the ticket that year, in his analysis.

But Republicans in Congress had hoped that reality, combined with the influence of the two former Republican House members in Mr. Trump’s cabinet — Tom Price, now head of health and human services, and Mick Mulvaney, his budget director — would have led to new conclusions. Social Security, health care and net interest now comprise nearly 60 percent of all federal spending, and that figure is expected to soar to 82 percent over the next 10 years; Mr. Mulvaney and Mr. Price have long been advocates for pruning.

This is not simply a fight for an ideological core — it is a question of what can pass Congress. A budget with no entitlement cuts and one that does not balance most likely has no chance of passing the House, and could be rejected by Senate Republicans, as well. Mr. Trump’s proposals are too far to the right in terms of domestic cuts and too far to the left in terms of balance.