By Jeremy Diamond, CNN

(CNN) -- A Republican resides in the White House. Republicans control the House and Senate. But most lawmakers who have filed into the White House this week to sit down with the President haven't been members of the Grand Old Party -- they've been Democrats.

This week, President Donald Trump has put more heft behind his hopeful rhetoric of a "different relationship" with Congress, discussing ways to move forward his legislative agenda with Democratic support and focusing on areas of agreement. The initiative follows last week's decision to support Democratic leaders' proposal to raise the debt ceiling for three months over the recommendations of Republicans.

But many wonder how effective his entreaties will be, as major pieces of legislation -- such as tax reform -- are only being crafted by Republican lawmakers.

On Tuesday night, Trump welcomed an equally split group of six GOP and Democratic senators to the White House to discuss tax reform. He then greeted eight House Democrats and five House Republicans to do the same on Wednesday. And on Wednesday night, Democratic leaders Sen. Chuck Schumer and Rep. Nancy Pelosi -- who have criticized Trump at every turn -- are joining the President for a private dinner at the White House.

"We should be able to come together to make government work for the people. That's why I was elected. That's why I ran," Trump said as he sat down with the House members.

On that front, Trump has offered indications he would support standalone legislation offering protections for young undocumented immigrants brought to the US as children -- a priority for Democrats -- despite first signaling that it would need to be tied to border security measures.

And he even appeared to shift the goalposts on tax reform following his discussions with Democrats, signaling Wednesday that he was open to to proposals that would see the wealthiest Americans pay more.

Sudden turn?

But Trump's sudden turn toward bipartisanship comes after the first eight months of his presidency were defined by bitter squabbles with Democrats and a near-singular focus on policies aimed at pleasing his political base.

It also occurs after months-long discussions with congressional Republican leaders on tax reform. Key Democrats, such as Oregon Sen. Ron Wyden who serves on the Senate Finance Committee, had yet to get a call from Trump.

Wyden pointed to the "irony" in that silence, given he has co-authored two bipartisan tax bills. While he said he hoped Trump was serious about a bipartisan push, he said an "awful lot of time has been frittered away" by not bringing Democrats into the fold earlier.

On that front, Trump has so far focused on courting moderate Democrats from states he won in 2016, far fewer than he would need to overcome the 60-vote hurdle to pass bipartisan tax reform.

The twist has left both Democrats and Republicans scratching their heads, unsure of the President's intentions.

"I don't think anyone on any side of the aisle can have any level of confidence on what to expect from the President," a Democratic leadership aide told CNN, noting that Trump is "quite impulsive."

A Republican leadership aide echoed the sentiment, pointing to Trump's seemingly spur-of-the-moment decision last week to side with Democrats -- over the objections of Republican leaders and his own Treasury secretary -- on a three-month deal that was widely panned by Capitol Hill Republicans.

While Republicans are still trying to divine the motives behind Trump's outreach, many are not altogether surprised given Trump's campaign promises to cut deals once he got to Washington -- and to compromise.

"It's Trump," the Republican leadership aide said. "He was never really bound to one party or another."

Democrats haven't had a seat at the table on tax reform as Republicans prepared to pass their proposals on a party-line basis, using the budget reconciliation process. Now, the White House is signaling a preference for a bipartisan deal.

"The President has been clear that his preference is to get tax reform done on a bipartisan basis," White House legislative affairs director Marc Short said Tuesday.

Republican support in the Senate was "not reliable" amid the Obamacare repeal debacle, prompting Trump to pursue Democrats, Short said. Those comments came despite White House officials promising for weeks the GOP-only budget reconciliation process would be the vehicle for tax reform.

'Why is he doing that?'

Some Republicans said they have only themselves to blame for the party's divisions and therefore they are understanding that Trump may see more of an opportunity to cut deals with Democrats now. Several Republican congressmen pointed to the Senate's failure to deliver the President enough votes to repeal Obamacare.

"Why is he doing that? Because he got rolled on Obamacare. We didn't come through with anything," said Rep. David Brat, a member of the conservative House Freedom Caucus.

Republican Rep. Tom MacArthur of New Jersey said he didn't fault Trump for cutting a deal with Democrats.

"I think he sent a strong message to Congress, 'Get things done or I'll work with other people,' " MacArthur said.

Republican Sen. John Thune, who attended the bipartisan dinner on Tuesday night, echoed that sentiment and said Senate Republicans' failure to deliver the votes on health care reform is now shaping Republicans' thinking.

"We have to get our act up here. We need to be able to deliver the votes," Thune said on MSNBC's "Morning Joe."

While skepticism about the President's commitment to a bipartisan path abounded in Washington on Wednesday, the Republicans and Democrats who attended the Tuesday night dinner seemed confident. They called the dinner meeting productive and substantive, signaling Trump's talk of bipartisanship might go beyond rhetoric and a three-month debt and budget deal.

Sen. Heidi Heitkamp, the North Dakota Democrat whose state overwhelmingly voted from Trump in 2016, even said the White House dinner "cemented" her decision to run for reelection in 2018, which she officially announced Wednesday.

"There is a real opportunity for those who want to find compromise in this country," Heitkamp said Wednesday on a local radio show.

The Democratic leaders heading to the White House on Wednesday night signaled other issues would animate their dinner with the President, but it was unclear whether Trump might bring up tax reform himself.

Some Republicans have questioned whether Trump has extended his hand toward Democrats not in the hopes of bipartisanship, but rather to increase the pressure on Republicans to deliver -- or risk more Democrat-aligned dealmaking.

Trump wasn't prepared to tip his hand on Wednesday.

"We're going to give it a shot," Trump said Wednesday of the bipartisan approach. "And if it works out, great. And if it doesn't work out great, hopefully we'll be able to do it anyway, as Republicans, OK?"

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