US President Donald Trump today vowed not to cut taxes for the wealthy, promised to try to protect young undocumented immigrants from deportation and extolled the virtues of bipartisanship, saying it had led to "some of the greatest legislation ever passed".

That he did all of that while declaring himself "a conservative" only heightened the sense of surrealism that has wafted through the nation's capital over the past eight days, as the President has expressed a newfound, if tentative, willingness to work across the aisle - a development that has left many Republicans chagrined and some Democrats cautiously optimistic.

Trump's outreach suggested that an unexpected deal he reached last week with Democrats may not have been an aberration.

This week's effort began yesterday at a bipartisan White House dinner with senators, proceeded to a gathering of House Democrats and Republicans today and was capped off by a presidential meal with the nation's two top Democrats, Senate Minority Leader Charles Schumer and House Minority Leader Nancy Pelosi.

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"Bottom line: There really is a new strategy coming out of the White House," said Congressman Henry Cuellar, a moderate Texas Democrat who had turned down previous White House invites but decided to attend today. "He meets with the bipartisan senators last night. He meets with us. He meets with Pelosi and Schumer today. There is a new strategy in place."

Congressman Tom Reed, (R), a Trump supporter who also attended today's gathering, said the President "has seen the theater up here and learned the lesson: Extremes on both the right and left are problematic to getting his agenda accomplished. You can't run a partisan bill to the finish line, so he knows he has to have his Plan B ready."

After eight months of pursuing a mostly hard-right, pro-Republican agenda with limited success, Trump is now flirting with fulfilling his campaign promises to govern as a bipartisan dealmaker.

In doing so, Trump could also be signalling the return of a recently bygone era when lawmakers of both parties dining - and working - with the president was hardly abnormal.

But, then, these are not normal times.

"It's up is down and down is up," said Jim Manley, a Democrat and former longtime Senate aide. "No doubt about it."

Last week, Trump shocked and angered Republican leaders by agreeing with Schumer and Pelosi to provide Hurricane Harvey relief while raising the federal borrowing limit and funding the government through December.

Then came the bipartisan dinner for senators, which included talk of infrastructure projects and featured three Democrats up for re-election in 2018 in states that Trump carried: Senators Joe Donnelly, Heidi Heitkamp, and Joe Manchin.

Several House Democrats expressed hope that they can work with the president.

"He was very explicit in saying that there would be no tax cut in this package for the wealthy," said Congressman Peter Welch, referring to a pledge by Trump that would mark a notable departure from his previous proposals. "At one point, he said they may have to pay a little more."

Trump has done little to reach out to Democrats until the past week and has often openly derided them and former President Barack Obama.

Trump has begun dismantling Obama-era regulations and protections on issues including healthcare, labour and the environment.

Last week, he also rescinded protections for 700,000 young undocumented immigrants brought to the United States as children and known as "Dreamers" - the same group he now says he wants to protect.

Even today, as the President played host to two bipartisan meetings, Trump and his team continued to equivocate. He expressed support for another Republican healthcare plan - spearheaded by Republican senators Bill Cassidy and Lindsey Graham - aimed at sharply curtailing Medicaid and other parts of the Affordable Care Act, commonly called Obamacare. In her daily press briefing, White House press secretary Sarah Huckabee Sanders argued that Trump is always working on behalf of Republicans.

"The President is the leader of the Republican Party and was elected by Republicans," Sanders said. "He beat out 16 other candidates to take that mantle on. And certainly I think one of the strongest voices. And so the idea that the Republican Party ideas are not represented in that room is just ridiculous."

Trump's reasons for engaging with lawmakers beyond the Republican leadership is deeply shaped by his experience on healthcare legislation, which has so far stalled in the Senate after months of fits and starts, according to two people familiar with the issue who have spoken with him recently.

Trump remains unhappy with GOP leaders for promising success earlier in the year, only to see the effort fall apart, said the people.

Trump now believes that Republicans - who control both the House and the Senate - cannot be trusted to carry bills to passage by themselves and views it as his burden to create a better environment for his legislative agenda to garner support. What matters to him, one Republican lawmaker said, is "putting wins on the board - not the specifics".

Instead of relentlessly courting members of the conservative, and often intractable, House Freedom Caucus, as he did on healthcare, Trump wants them to "feel the burn a little bit," the lawmaker added, framing the new outreach as Trump's way of reminding conservatives in both chambers that he likes them but does not need them.

"They're not the only player he's willing to play with," said Michael Steele, the former Republican National Committee chairman. "He's saying to them, 'I'll be a free-range president.' "

Senator Ron Johnson, (R), who attended yesterday's dinner, said jump-starting talks on tax cuts and other potential changes remains at the top of Trump's agenda. He said Trump wants to focus cuts on brackets that affect middle-class people.

"Let's face it: If you want tax reform, you want to avoid pitfalls that make it impossible," Johnson said of Trump's approach on this priority. "Selling tax cuts for the wealthy is pretty impossible."

"What I saw from the President was a genuine process to find bipartisan agreement on taxes and infrastructure," Johnson added. "My guess is some Democrats definitely agree with him."

Manchin said the dinner was "a very good, productive meeting," and said he believes the president, who was once a registered Democrat, is simply entering his legislative comfort zone.

"The President seemed more at ease, more comfortable, talking about finding a bipartisan solution than trying to have to defend a rigid, one-side-only works," Manchin said. "I think he's able to approach legislation in a total sphere, not just one side."

Moderate Republicans, in particular, have cheered this development, after long feeling sidelined inside the House as Freedom Caucus members and other conservatives have rebelled against their party's leadership.

US President Donald Trump speaks during a meeting with a bipartisan group of lawmakers in the Cabinet Room of the White House. Photo / AP
US President Donald Trump speaks during a meeting with a bipartisan group of lawmakers in the Cabinet Room of the White House. Photo / AP

Trump's conservative critics, however, said his latest gestures reflect his liberal instincts on some issues and his intense desire for popularity.

"He's always had that itch to liberate himself from the Republican Party," said William Kristol, a Trump critic and editor at large of the Weekly Standard magazine. "He ran against it in 2015 and 2016, and has attacked it in 2017. He wants to win and doesn't care about the substance of winning."

Kristol added, "Democratic voters may loathe Trump, but he could conceivably give them lots of policy victories."

Democrats say they are focused only on working with the President on areas where they believe they can get what they want in terms of their priorities, including protections for the Dreamers and federal healthcare subsidies for Obamacare.

They have vowed not to trade Dreamer protections for Trump's long-promised wall at the southern border - and in recent days the White House has indicated the two issues do not have to be linked.

On other issues and with this president, many Democrats remain wary.

Donnelly, despite being wooed by Trump and up for re-election next year, said he feels no pressure to vote for the Republican tax plan if he thinks it's a bad deal.

"If the tax package makes sense, I'll support," Donnelly said. "If not, I'll pass."