House Speaker Paul D. Ryan (Wis.) showed the president glossy photos of a wall under construction along the U.S.-Mexico border.

Senate Majority Leader Mitch McConnell (Ky.) brought an article from the Washington Examiner that described Trump as brilliantly handling the current budget process, and portrayed the GOP as unified and breaking through years of dysfunction.

Their message, according to two people briefed on the meeting: The budget process is going smoothly, the wall is already ­being built, and there’s no need to shut down the government. Instead, they sought to persuade Trump to put off a fight for more border wall money until after the November midterm elections, promising to try then to get him the outcome he wants, according to the people, who spoke on the condition of anonymity because they weren’t authorized to reveal details of the private discussion.