The resulting furor led to an effort by the campaign manager, Brad Parscale, to tighten control. By removing several pollsters, the campaign hopes to shrink the circle of outside operatives who have access to information that could leak, according to the presidential adviser, who was not authorized to speak publicly.

The rupture of the team came even as the president and his advisers were preparing for a large and elaborate rally in Orlando, Fla., on Tuesday night to formally open his campaign for a second term. Mr. Trump was hoping for a show of strength as Democrats had drawn increasing attention before their first debates on June 26 and 27.

The internal poll numbers, while not predictive, painted a bleak picture of the current state of the race for Mr. Trump, at least against Mr. Biden, when they were taken in March. They showed a number of critical states at risk — not just Florida and the Midwestern states, but even some longtime Republican bastions like Georgia. A Democratic state that Mr. Trump’s aides have insisted they want to put in play, Minnesota, appeared out of reach for the president.

The polling was reported on by The Times nearly two months ago without citing specific numbers. Last week, The Times reported that Mr. Trump had told aides to deny that such polls existed and to say that other data in the survey showed him doing well.

Some aides to the president appeared to be using the episode to undermine one of his closest advisers, Kellyanne Conway, who was Mr. Trump’s final campaign manager in 2016 and is now his White House counselor. Ms. Conway’s relationship with Mr. Trump, and the praise he has given her for his 2016 victory, have long stirred envy among other advisers to the president. Her former firm, the Polling Company, was one of the ones to be ousted. Ms. Conway no longer has any formal ties to the company, which was sold in 2017 to CRC Public Relations, a well-known conservative advocacy firm.