Dramatic testimony before Congress. Combative public hearings. Damaging leaks. Continuing investigations.

As the controversy surrounding the White House continues, the road ahead is a series of pitfalls for Republicans that will be nearly impossible to escape.

The turmoil will hobble their ability to enact legislation and could ultimately jeopardize their hold on Congress.

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Related: Who is Robert Mueller? A primer on the Trump-Russia probe's new player

U.S. President Donald Trump struck back at critics and attempted in vain to change the topic on Thursday. He wrote on Twitter that the investigation into possible collusion between his campaign and Russia represents "the single greatest witch hunt of a politician in American history!"

He also flatly denied he had asked the country's top law-enforcement officer, Federal Bureau of Investigation director James Comey, to shut down a portion of the Russia investigation in February.

Any talk that he had engaged in criminal behaviour was "totally ridiculous," Mr. Trump told reporters. "We have to get back to running this country really, really well."

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Mr. Trump departs Friday for his first foreign trip as President, a nine-day journey to Israel, Saudi Arabia, Italy, the Vatican and Belgium. The trip represents a chance for Mr. Trump to shift the focus of daily headlines after more than a week of raging controversy, which began when the President fired Mr. Comey, the person overseeing the Russia probe.

But any break in attention to the topic is likely to be short-lived. Robert Mueller, a former FBI director highly respected by both parties, was named special counsel on Wednesday to oversee the investigation into what is becoming a hydra-like scandal absorbing increasing amounts of legislative time and energy.

Mr. Mueller will continue the original subject of the federal investigation, which is to examine Russia's efforts to meddle in the 2016 presidential election and determine whether Mr. Trump's advisers colluded with the Kremlin.

However, the controversy has ballooned to include Mr. Trump's own actions in response to the probe. They include firing Mr. Comey and allegedly telling him to shut down a portion of the investigation involving Mr. Trump's former national security adviser, Michael Flynn.

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Every passing day brings a fresh revelation. On Thursday, Reuters reported that Mr. Flynn and other advisers to Mr. Trump's campaign were in contact, via telephone and e-mail, at least 18 times with Russian officials and others with ties to the Kremlin in the last months of the presidential race.

Prior to being named national security adviser, Mr. Flynn told Trump transition officials he was already under federal scrutiny for secretly working as a lobbyist for Turkey, the New York Times reported late Wednesday. Mr. Flynn allegedly told friends last month he was still in contact with Mr. Trump, who urged him to "stay strong" in the face of the investigation, according to a report Thursday from Yahoo News.

For Republicans, it is a crisis that will drag on. Each new twist of the controversy keeps it in the spotlight, distracting from their broader agenda. But they will not break with Mr. Trump unless his supporters abandon him, or unless there is incontrovertible evidence of wrongdoing by the President.

"I don't think there's a way out," said Robert Jervis, an expert in national security policy at Columbia University. "I can't see anything that would make [the controversy] go away. The Republicans have to prepare for a long period of torture."

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In addition to what has become a daily cascade of leaks to the media, Republicans are confronting a series of made-for-television events related to the Russia controversy. Mr. Comey, for instance, is expected to testify under oath before Congress about the events leading to his firing and his conversations with Mr. Trump.

The President, meanwhile, will announce his selection for Mr. Comey's replacement shortly, with the leading candidate reportedly Joe Lieberman, a former Democrat-turned-independent senator. The new FBI director will face confirmation hearings, which will provide a fresh opportunity to maintain attention on the Russia investigation.

"It's going to be very hard for Republicans to avoid this [controversy]," said David Leviss, a partner at O'Melveny and Myers in Washington who formerly served as an investigator for two congressional committees. "And it's hard to see how they make progress on the big legislative initiatives that seem to be their priority, like health care and tax reform."

Lawmakers are also watching the political winds ahead of the midterm elections next year. If Republicans break with Mr. Trump, they risk incurring the wrath of his supporters and spurring a primary challenge. Midterm elections, which have lower turnout than presidential votes, often hinge on which party's voters are more motivated to show up – and Democrats appear to hold the advantage in that regard.

For the foreseeable future, the Russia probe will proceed on two related but separate tracks: the investigation overseen by the special counsel and the multiple probes under way in Congress. Each has a distinct purpose, said John Barrett, a law professor at St. John's University in New York who formerly worked for the independent counsel who investigated the Iran-Contra affair during the Reagan administration.

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The special counsel's job is to investigate potential crimes and decide whether prosecutions are warranted, while it is the responsibility of lawmakers to hold officials responsible and exercise oversight of government. Neither process is likely to conclude quickly, Prof. Barrett said. "Nobody's going to be done in two weeks or two months."

With a report from Adrian Morrow in Washington