Trump made his comments during a White House Cabinet meeting as Democrats sought to build public support for their fast-moving impeachment inquiry and the administration pressed its efforts to stonewall the probe.
House Speaker Nancy Pelosi issued a video and "fact sheet" that may give hints about the articles of impeachment - formal charges - Democrats may pursue against Republican Trump, accusing him of abuse of power, a "shakedown" involving Ukraine and a cover-up.
Republicans in the House of Representatives tried to censure one of the inquiry's leaders, House Intelligence Committee Chairman Adam Schiff, but the motion was blocked by Democrats who control the chamber.
Few Republican lawmakers have shown an inclination to remove Trump from office even as Democrats focus on his pushing a vulnerable foreign ally to interfere to his benefit in the 2020 US election by providing political dirt on Joe Biden, a leading contender for the Democratic presidential nomination to run against Trump in November.
Senator Mitt Romney is one of the few Republicans who have sharply criticized Trump, who has denied wrongdoing.
Other Republicans have expressed misgivings about Trump policies, including criticism from Senate Majority Leader Mitch McConnell and Senator Lindsey Graham of his withdrawal of US troops
Approval of articles of impeachment in the House would prompt a trial in the Republican-led Senate on whether to remove Trump from office.
"The Republicans have to get tougher and fight. We have some that are great fighters, but they have to get tougher and fight, because the Democrats are trying to hurt the Republican Party before the election," Trump said.
Trump said the Democrats are "vicious and they stick together."
"They don't have Mitt Romney in their midst. They don't have people like that. They stick together," Trump added.
In an interview aired with "Axios on HBO," Romney denounced Trump's requests to Ukraine and China to investigate Biden, questioned Trump's character, criticized his decision to "abandon" Kurdish allies and deplored his hush money payment to an adult film star.
Romney was the 2012 Republican presidential nominee but lost to incumbent Barack Obama.
ANTI-CORRUPTION PROVISION
Trump also labeled as "phony" an anti-corruption clause in the US Constitution that Democrats have accused him of violating by profiting from his businesses, including a hotel in downtown Washington. The so-called emoluments clause bars a president from receiving any gifts, payment or other things of value from a foreign country.
An accusation of violating the emoluments clause could figure into the articles of impeachment against Trump.
Democrats mocked the president over the issue.
"It is literally in the Constitution," Democratic congressman Eric Swalwell said on Twitter.
Asked if it is a foregone conclusion that House Democrats will vote to impeach him, Trump said: "They want to impeach. And they want to do it as quick as possible."
At the heart of the inquiry is a July 25 phone call in which Trump asked Ukrainian President Volodymyr Zelenskiy to investigate Biden and his son Hunter, who had been a director of a Ukrainian energy company, as well as a discredited theory that Ukraine, and not Russia, interfered in the 2016 US election.
Another round of testimony in the inquiry is set for this week, including by Bill Taylor, the top US diplomat in Ukraine, on Tuesday.
Acting White House budget director Russell Vought said both he and Michael Duffey, associate director for national security programs at the Office of Management and Budget, would not provide depositions to the committees leading the inquiry.
Duffey had been scheduled to testify behind closed doors on Wednesday as Democrats investigate whether Trump withheld $391 million in security aid to Ukraine to pressure the country to investigate Biden and its own role in the US election.
A planned deposition on Wednesday by Philip Reeker, the acting US assistant secretary of state for European and Eurasian affairs who oversaw US policy toward Ukraine, has been postponed at the request of the lawmakers carrying out the inquiry and no new date has been set, a source familiar with the matter said.
Trump, a real estate developer, said serving as president has personally cost him $2 billion to $5 billion dollars. He also expressed annoyance at having to reverse his decision to stage the Group of Seven summit in June at his Trump National Doral golf resort in the Miami area.
His plan to host the gathering was lambasted by both Democrats and Republicans who said it gave the impression he was profiting from being president.
"I would've made a fortune if I just ran my business. I was doing it really well. I have a great business. I have the best properties," Trump told reporters.