President Donald Trump on Thursday left members of both political parties unsure of his next move on immigration policy, as he repeatedly defended his latest talks with senior Democrats, but left open the question of whether a deal could be reached about the fate of illegal immigrant "Dreamers" in the United States, leaving some Republicans in Congress wary and unsettled about Mr. Trump's plans.

"Typically, a President of our party would work with our party on a proposal that we would be supportive of," said Rep. Pete Sessions (R-TX), the Chairman of the powerful House Rules Committee.

Speaking to reporters off the House floor, Sessions said GOP lawmakers were still trying to figure out the President's overall strategy when it comes to negotiations with Congress - which in the last two weeks have been focused more on Democrats than Republicans.

"So, we're learning now how he wants to operate," Sessions added in a measured tone of voice.

The uncertaintly felt by Republicans - was also one felt by Democrats - and was fueled throughout the day by the President, as he put out a variety of messages on immigration that were seemingly at odds.

Before sunrise, Mr. Trump tweeted that there had been no deal reached with top Democrats in Congress about the fate of "Dreamers" under the DACA program, which shielded some 800,000 younger immigrants from being deported.

A few minutes later, the President made clear that he was not in favor of deporting those "Dreamers," saying in a tweet, "Does anybody really want to throw out good, educated and accomplished young people who have jobs, some serving in the military?"

Not even two hours later, the President told reporters that he was close to reaching a deal with Democrats on the DACA issue, making clear that he could accept the idea of a new law on that subject, in exchange for tougher controls on the border.

As for money for his border wall, the President stated, "the wall will come later," which was basically what leading Democrats had said they had agreed to at a dinner on Wednesday night at the White House.

But then, on Air Force One, the President sent a different message, telling House Speaker Paul Ryan by telephone that no deal had been struck with Democrats, that his dinner with House Democratic leader Nancy Pelosi and Senate Democratic Leader Charles Schumer was just a 'discussion,' not a negotiation.

That message was sent to the Speaker by both the President, and the White House Chief of Staff.

But the President wasn't done.

Later, after touring damage in Florida from Hurricane Irma, the President met with reporters for 15 minutes aboard Air Force One, and was asked about the DACA issue, and his outreach to Democrats.

"Well, many Republicans really like it," the President said about DACA. "Many of them agree with what I'm doing."

Asked about the legislative struggle with health care, the President made clear he did not regret his effort to woo Democrats on immigration, tax reform and more.

"And if the Republicans don't stick together then I'm going to have to do more and more," Mr. Trump said, holding out the possibility of more deal-making with Democrats.

But as soon as the President returned to the White House, he added in another wrinkle to the DACA debate, suddenly saying that he was not for a path to citizenship - not for amnesty - for those immigrant "Dreamers."

The up and down nature of the day left Democrats wondering what Mr. Trump might or might not support, and again had Republicans wondering what was in their future - for a President of their own party.

"If they see amnesty coming out of the White House, then that is one thing that will crack his base," said Rep. Steve King (R-IA), who has championed the President's tough talk on illegal immigration, which attracted a number of votes in 2016.

"They came on board because of build a wall, enforce the border, enforce immigration law, no amnesty," as King rattled off familiar campaign points from Mr. Trump.

The machinations on DACA came in the wake of last week's surprise deal between the President and top Democrats in Congress, on an aid bill for victims of Hurricane Harvey - which also included a short term extension of the national debt, and a temporary federal spending plan that runs until December 8.

While that was hard to swallow for a number of Republicans in Congress, waking up to news on Thursday about a possible DACA deal - and no money for a border wall - created even more cognitive dissonance for the GOP.

To be fair, there were some Republicans who brushed off the latest outreach by Mr. Trump to Pelosi and Schumer.

"It doesn't worry me at all," said Rep. Markwayne Mullin (R-OK), who said he had been assured by top Republicans that the President was not going to sell out the GOP.

"As long as we put conservative values and conservative ideas and roll back the last eight years of the Obama Administration, them I'm all on board," Mullin added.

But for Republicans, that was the open question - would the President stick with conservative solutions - or cut more deals with the Democrats, pulling Mr. Trump more to the middle.