He also singled out other favorite Democratic targets, including former President Barack Obama, former Secretary of State Hillary Clinton, Representative Adam B. Schiff of California, Senator Elizabeth Warren of Massachusetts and Mr. Biden.
Mr. Trump’s trip to Texas stirred interest among political strategists because the state has long been a bedrock for Republican presidential candidates and is therefore not a battleground that attracts as much campaigning. In devoting a day here headlining a fund-raiser in Fort Worth and cutting the ribbon on a new Louis Vuitton workshop in Keene, Mr. Trump prompted Democrats to declare that he must be worried about losing the state.
For Democrats, Texas has been the elusive holy grail for years, always supposedly close to flipping from red to blue yet remaining out of reach. Texas has not supported a Democrat for president since 1976 or for any statewide office since 1994. But as the state’s demographic makeup shifts, Democrats insist change is inevitable. Mr. Trump won the state in 2016 by nine percentage points, the first single-digit margin at the presidential level in 20 years, and Mr. O’Rourke came within 2.6 points of unseating Senator Ted Cruz last year.
A poll last month showed that Mr. Trump could be in trouble this time around. Forty-eight percent of Texans surveyed by Quinnipiac University said they would definitely not vote for him next year while only 35 percent said they would definitely support him and 14 percent said they would consider it.
But the president’s campaign team scoffed at what it called Democratic wishful thinking, saying that the only reason Mr. O’Rourke came close last year was because Mr. Trump was not on the ballot. Tim Murtaugh, his campaign spokesman, said the president made the trip on Thursday not out of concern but to connect with his strongest backers.
“You’ve got to campaign and go show love to the people who got you there,” Mr. Murtaugh said. Rather than be turned off by the impeachment battle, he said, Mr. Trump’s base has been energized. “I didn’t think it was possible for the president’s supporters to be more engaged, but impeachment has achieved that,” he said.
Mr. Trump declared that Texas would remain in his column. “Texas is not in play,” he said.
Maggie Astor contributed reporting from New York.