But this plan — a product of a collaboration between the Office of Management and Budget director, Mick Mulvaney; the National Economic Council director, Gary Cohn; and the White House chief strategist, Stephen K. Bannon — is intended to make a big splash for a president eager to show that he is a man of action.

Mr. Trump’s top advisers huddled in the White House this weekend to work on his Tuesday night prime-time address. They focused on a single, often overlooked message amid the chaos of his first weeks in the White House: the assertion that the reality-show candidate is now a president determined to keep audacious campaign promises on immigration, the economy and the budget, no matter how sloppy or disruptive it looks from the outside.

“They might not agree with everything you do, but people will respect you for doing what you said you were going to do,” said Jason Miller, a top communications strategist on the Trump campaign who remains close to the White House.

“He’s doing something first, and there’s time for talk later,” Mr. Miller added. “This is ultimately how he’s going to get people who didn’t vote, or people who didn’t vote for him, into the fold. Inside the Beltway and with the media, there’s this focus on the palace intrigue. Out in the rest of the country, they are seeing a guy who is focused on jobs and the economy.”

The budget plan, a numerical sketch that will probably be substantially altered by House and Senate Republicans — and vociferously opposed by congressional Democrats — will be Mr. Trump’s first big step into a legislative fray he has largely avoided during the first 40 days of his administration.