Welcome home, Mr President. It has become worse while you were away.

Problem-plagued presidents love to travel abroad, to be welcomed by overhead jets, sword dances and lots of pomp and photo-ops. But then they have to return. When President Donald Trump comes home this week, he will have to confront the reaction to his widely ridiculed budget. He will have to deal with the struggle by congressional Republicans to patch together a politically unpopular healthcare Bill, a government with scores of high-level vacancies and a White House wracked by dissension and leaks.

Above all, he will face the agony of a special counsel’s investigation that could imperil his presidency. The inquiry by Robert Mueller into Russian interference in the 2016 election is deadly serious, and is likely to be wide-ranging and protracted. That is why the President and some of his associates are, in investigative parlance, “lawyering up”.

Officially, Mueller is answerable to Deputy Attorney-General Rod Rosenstein, but his standing is such that the only limit to his investigative power is Trump’s authority to decide he is a threat and fire him. The former director of the Federal Bureau of Investigation, Mueller is empowered to look into links between Russians and the Trump universe. This includes “any matters” that arise from the investigation.

Mueller can be counted on to be discreet, fair and tough. He will look at whether there was any co-ordination between Russian authorities and campaign personalities, any financial links or money laundering, and whether the President tried to obstruct the investigation.

Evidence so far is only circumstantial. Yet there is plenty of it, including a pattern of deceptions and lies about Russian connections that causes Republican concern.

Former FBI director James Comey, fired this month by Trump, kept contemporaneous notes on private conversations in which the President reportedly sought to sidetrack the investigation into his former national security chief, Michael Flynn. Comey soon will brief Mueller.

Perhaps most worrisome to the President’s allies was Trump’s call to two top intelligence officials to pressure the FBI to curb the Russia inquiry.

That call has invited comparisons to President Richard Nixon’s obstruction of the Watergate investigations. It is unlikely that there will be anything this time like the “smoking gun” White House tape recording from 1972, in which Nixon discussed using the Central Intelligence Agency to shut down the investigation. Remember, though, that the House Judiciary Committee had voted on a bipartisan basis to impeach Nixon for obstruction nine days before the smoking gun tape came out.

The reckless Trump could expose himself to further risks. President Bill Clinton’s dalliance with an intern, which precipitated impeachment proceedings, occurred 15 months after the 1994 appointment of Kenneth Starr as independent counsel to investigate financial transactions that took place during Clinton’s days in Arkansas years before.

The allegations of financial links between the Trump campaign and the Kremlin, which Trump adamantly denies, call to mind allegations compiled by Christopher Steele, the retired Russia-desk chief of Britain’s MI6 intelligence agency.

Steele compiled a dossier at the behest of Trump’s US political opponents, which, drawing on Russian sources, concluded that Moscow and Trump had deep connections. Its contents remain unverified and it has been debunked by Trump supporters. But intelligence agencies are continuing to pursue some of the specifics.

US intelligence agencies reported in January that the Russian President, Vladimir Putin, ordered an influence campaign of cyberattacks and fake news to undermine Hillary Clinton’s presidential prospects and public faith in the democratic process. Their report did not comment on whether anyone in the Trump campaign communicated with Russian operatives.

What are Republicans doing and thinking about Mueller’s inquiry into that question and related ones? Some in Congress, from the predictable and hyperpartisan Trey Gowdy to the more independent Senator Charles Grassley, have tried to discredit the investigation. They have not gotten any traction.

Privately, more and more Republicans expect the Trump-Russia scandal to mushroom.

They recognise that Trump has made dangerous enemies by offending the intelligence community and, with the sacking of Comey, the FBI. They worry about whether they can escape the fallout.

•Albert R. Hunt is a Bloomberg View columnist. He was the executive editor of Bloomberg News, before which he was a reporter, bureau chief and executive Washington editor at The Wall Street Journal