President Trump touted his power in his second go-around in the White House Saturday while rallying in Kentucky to bolster Republican turnout as his party struggles in the midterms, saying, “I can do stuff that is unbelievable.”

Mr. Trump, who spoke in the city of Highland Heights to boost Republican candidates, including Ed Gallrein for the U.S. House, was riffing on his decision to change how the U.S. government refers to the Gulf of Mexico to the Gulf of America.

“I don’t think I could have done this in my first term. This is a much more powerful term,” Mr. Trump said. “Google wouldn’t have taken my call in the first. Now, they kiss my ass.”

“Well, I also changed the name of a lake in Canada to the Lake America,” he continued, referring to Lake Ontario.

Mr. Trump’s self-proclaimed power is set against voter frustration with how he’s wielded it, with tariffs and the Iran war driving up prices and more Americans seeing the president looking out for his own interests and not those of the country.

With control of both chambers of Congress on the line, and with it the prospects of Democratic-led investigations of his administration should they win, Mr. Trump has put himself at the fore for voters even as Republicans privately worry he’s a liability.

Mr. Trump nominated one of his personal lawyers to serve as attorney general, ordered military strikes on accused drug-smuggling boats, is trying to put his name on the Kennedy Center, and has enriched himself and his family while he’s been in office.

While meandering through topics onstage in Kentucky, Mr. Trump touched on gas prices, saying that the war with Iran was going to end soon — an assertion he’s made many times over the course of the nearly eight-month conflict — and that gas prices will drop to lower than previously. The crowd cheered.

Mr. Trump rehashed his dubious promise that if Republicans win the House and the Senate, then every adult American would get $5,000. That would most likely cost more than $1 trillion and require congressional approval, while exacerbating the country’s nearly $1.8 trillion annual budget deficit.

At Saturday’s rally, Mr. Trump added a new conditional promise for Kentucky; if Republicans win, he said, the Department of Defense would invest in revitalizing a drug manufacturing facility in the state.