The prospect of Donald Trump's impeachment is looking unlikely with Democrats divided over the issue, but the president may end up nudging them closer with the words "I don't do coverups."

Trump abruptly walked out on a meeting about infrastructure with Democratic House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer on Wednesday, refusing to negotiate on policy until Democrats stop investigating him.

His statement drew immediate comparisons to Richard Nixon's infamous "I am not a crook" denial, which came months before Congress initiated formal proceedings to level charges against him over the Watergate scandal.

"Obviously, any time the president has to say he's not a crook, he's got a problem. And there is definitely a parallel here between 'I am not a crook' and 'I don't do coverups,'" said Washington-based Democratic strategist Rachel Gorlin.

Trump uttered his defiant one-liner during a surprise Rose Garden speech lashing out at House Democrats trying to investigate him for obstruction of justice. He refused to resume talks with Democrats on a $2-trillion infrastructure bill that he himself wanted to craft.

"I walked into the room and I told Leader Schumer and Speaker Pelosi I want to do infrastructure," Trump told reporters in the Rose Garden. "But you know what? We can't do it under these circumstances. So get these phoney investigations over."

House Speaker Nancy Pelosi and Senate Democratic Leader Chuck Schumer, right, speak to the media along with other Democratic lawmakers after a failed meeting with U.S. President Donald Trump to discuss infrastructure in Washington. The Democratic caucus is split over the question of whether to initiate impeachment proceedings against Trump. (Jonathan Ernst/Reuters)

Earlier, Pelosi had charged that Trump "is engaged in a coverup" over the Mueller Russia investigation. She doubled down later, adding that evidence suggesting Trump obstructed justice could amount to "an impeachable offence."

Trump has already ordered his former White House counsel Don McGahn to defy a subpoena from the House to testify before the judiciary committee. But the more that Trump stonewalls the Democrats, the more inclined members of Congress might be to press for his impeachment.

Holding legislative activity hostage

Which is why Wednesday's ultimatum and refusal to discuss policy with Democrats feels so risky, Gorlin said.

"Trump is willing to hold all legislative activity up, willing to hold it hostage to ending congressional investigations. And that is way beyond anything we've ever seen and I can say that with some confidence."

Whether Trump's rebuttal ushers in impeachment proceedings, as it did in Nixon's case in the 1970s, will be left to the political winds. So far, it doesn't look likely.

Trump has already ordered his former White House counsel Don McGahn to defy a subpoena from the House to testify before the judiciary committee. Elizabeth Warren, right, is the first Democratic presidential candidate running for 2020 who has explicitly called for the start of impeachment proceedings. (Lucas Jackson, Yuri Gripas/Reuters)

Before Trump's Rose Garden remarks, House Democrats met to discuss the possibility of impeachment, though Pelosi and other senior members have been unwilling to pursue that course. Older members would be understandably gun-shy. They still recall how the 1998 impeachment of Democratic president Bill Clinton on perjury and obstruction charges boomeranged badly on the Republicans in the next election, as they were seen as overreaching.

If Trump removes any hope for Democrats being able to do something about health care or infrastructure, they have nothing else to do with their time but pursue impeachment - Colin Strother, Democratic strategist

Colin Strother, a Democratic strategist in Texas, expects Trump's latest act of resistance against ongoing investigations might backfire.

"The Speaker's message has been we've got to focus on the issues that people care most about, not impeachment," he said. "If Trump removes any hope for Democrats being able to do something about health care or infrastructure, they have nothing else to do with their time but pursue impeachment."

Impeachment could — but likely won't — trigger Trump's potential removal from office, due to a Republican-dominated majority in the Senate. If Trump is unlikely to be ousted anyway, the thinking goes, impeachment looks to be a fool's errand.

A shifting political consensus might change things. One Republican representative, Michigan's Justin Amash, has called for impeachment. If other conservatives join in, as well as veteran Democratic lawmakers like House Majority Leader Steny Hoyer, the momentum could be too much to ignore.

Watch: Trump's impromptu Rose Garden news conference

Trump said he wouldn't work with Democrats on infrastructure, given coverup accusations 12:01

Gorlin said there is no magic number for "broad-based support," but if, say, 50 per cent of independent voters begin demanding impeachment, that may be a strong enough tide to ride toward impeachment, she said.

A Reuters/Ipsos online poll this month found that 45 per cent of Americans believe Trump should be impeached. Polling from October 1973, four months before the start of Nixon's impeachment proceedings, found 44 per cent of respondents wanted him impeached, out of 947 adults interviewed.

Ross Baker, a congressional expert who teaches U.S. politics at Rutgers University, doubts Congress is ready to take such a precipitous step. At least not without some kind of "larger-calibre" smoking gun such as a possible refusal by Trump to obey a future court order, or proof that he committed serious financial crimes.

Vulnerable Democrats fear backlash

As for all the loud progressive voices pushing for impeachment, he said, freshmen Democrats elected in vulnerable states are trying to dampen the voices of louder pro-impeachment representatives like New York's Alexandria Ocasio-Cortez and Michigan's Rashida Tlaib.

"Which one of these House members from a swing district is going to be first to come out and openly state he or she is ready to go ahead with impeachment?" he said. "Certainly some members of that class of 2018 are flat-out opposed to it."

Watch: Nancy Pelosi and Chuck Schumer react on Wednesday

Nancy Pelosi and Chuck Schumer made a statement on Wednesday in Washington 8:16

Congressional researcher Matt Glassman, a senior fellow at Georgetown University's Government Affairs Institute, dismisses the theory that Trump may be trying to goad Democrats into impeaching him in order to reap the political gain.

That strategic argument is rooted on flawed logic, he said, namely because "narcissism and pride" would be reasons enough for the president not to want to blemish his presidency.

"Even if you knew you would survive [impeachment], it's not the badge of honour you're looking for," Glassman said. "These theories of a presidential master plan, of four-dimensional chess, that's implying a coherent strategy on the part of Trump that I just don't see."

In the meantime, Trump's evasiveness is bound to annoy members of Congress who see their powers of oversight being squeezed by the executive. Refusing to talk policy with Democrats is "adding pieces to the impeachment push," Glassman said.

If it's strategy, it's puzzling at a time when the president could have scored an easy win on reaching a bipartisan infrastructure deal.

"It's a strange threat for him to make: 'If you don't stop investigating me, I won't do this thing that would help me,'" Glassman said.

"He just can't stop talking about it. He's fixated on these investigations because they're about himself, when normal advice would be to ignore the scandals and focus on policy. Trump is doing exactly the opposite."