Washington (CNN) Donald Trump is facing growing resistance from Republican lawmakers who are both turned off by his chronically chaotic style and increasingly unafraid of his ability to punish them politically as the President's poll numbers plummet.

Trump's diminishing influence was on stark display last week when his top priority -- the repeal and replacement of the Affordable Care Act -- failed dramatically in the Senate. Emboldened congressional Republicans are also pushing back on a range of issues including Russia, transgender rights, health insurance subsides for low income Americans, and even whether to reform Senate rules to make it easier for the GOP to pass his agenda.

The President, still resentful after signing a bill Wednesday that placed new sanctions on Russia for election meddling -- and restricted his own ability to ease punishments in place against Moscow -- underlined the public discord Thursday morning.

"Our relationship with Russia is at an all-time & very dangerous low. You can thank Congress, the same people that can't even give us HCare!" he tweeted.

Sen. John Cornyn of Texas blamed "so much chaos and confusion" at the White House for the disconnect between 1600 Pennsylvania Ave. and the GOP-controlled Congress. The second-ranking Senate Republican said "communication and coordination" between the Trump White House and Republicans on the Hill are "suffering" and hopes the addition of Gen. John Kelly as the new chief of staff will help.

"I think Gen. Kelly is a big step in the right direction in organizing the administration so we can coordinate our activities better," Cornyn told CNN. "People like me, we want him (the President) to be successful because I believe in the policies he ran on and won on. But it is hard when there is so much chaos and confusion."

Sen. Lindsey Graham, R-South Carolina, agreed that Kelly could be a "calming influence," something that might help as the White House, Congress and the Pentagon decide what to do about transgender service members who Trump unexpectedly announced in a tweet would no longer be welcomed in the military.

"We're not going to change transgender policy based on a tweet. If there's a change, it will be based on facts and circumstances and recommendations from the Department of Defense," Graham said in an interview with CNN's Kate Bolduan. "We're going to be very professional."

Two senior Republican aides on Capitol Hill downplayed the talk of a new divide between the White House and Senate Republicans. One aide said it's rather a sense of frustration over the White House not focusing on the agenda and "constantly talking about random things that cause one distraction after another."

There are signs that Trump is adjusting his approach with lawmakers. Trump invited Sen. Rob Portman, an influential and policy-oriented Republican from Ohio, to the White House Wednesday, the latest in a series of one-on-one meetings he has hosted with GOP senators in the past week.

A senior White House official said the President is stepping up his outreach to Senators and House members as a realization that their fates are connected and they need to work together on the agenda, particularly as deadlines approaches on the debt limit, government spending bill, and other must-pass measures.

Still, many Hill Republicans are mystified why Trump hasn't taken a more "professional" approach, as Graham described it, to the myriad of tough policy issues before them.

The recent battle on health care, for example, gave rise to several high-profile incidents in which Republicans blatantly stood against the President.

For instance, when the bill failed, Republican leaders were ready to "move on," in the words of Senate Majority Leader Mitch McConnell, and come back to health care when and if they could devise a policy that could pass. But Trump, using Twitter, browbeat Senate Republicans to skip their recess and keep trying, something GOP leaders never seriously contemplated doing, according to a GOP leadership aide

Some senators appear perfectly content in their willingness to stray from the party line.

Despite facing threats from Trump's administration, Sen. Lisa Murkowski of Alaska -- a moderate Republican who's been known to break with her party on big legislation -- voted against the Republican health care plan and returned to her home state over the weekend, where she said she was met with "an outpouring of support and thanks and tears" at airports.

With a noticeable spring in her step, Murkowski told reporters on Tuesday that the response she got from voters only "reinforced" her position that Republicans need to hold a more open and transparent process next time.

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Realistic advice for GOP?

Also on health care, Trump pressed the Senate to change rules to weaken the filibuster and ease passage of the bill by requiring only 51 votes. But Republicans already were using special rules to do just that and thus make health care filibuster-proof, so Trump's admonition was dismissed by GOP senators who knew better.

Many Republicans are also taking a longer view and resisting Trump's call for a permanent change to the filibuster, knowing it's something that will benefit them when they are no longer in the majority.

"The Senate should not go to a 51-vote majority for every vote. Because the Senate is the one entity in the federal government where the minority view is heard and deliberation is protected," said Sen. James Lankford, R-Oklahoma, in an Wall Street Journal opinion article in which he urged some reforms to the how the Senate could speed some of its work while preserving this important tool that protects minority rights.

Without a new health care bill firmly in the works, Republican senators are openly rebelling against Trump on the issue. Rather than working on comprehensive legislation, they are scheduling hearings in a bipartisan manner to extend the existing health care law's subsidies for low-income Americans paid to insurance companies that Trump railed against.

"Without payment of these cost-sharing reductions, Americans will be hurt," Senate health committee Chairman Lamar Alexander, R-Tennessee said while announcing a hearing on the issue.

That contrasted with Trump's recent demand that Republicans "let Obamacare implode."

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Arizona politics

Perhaps the most overt revolt last week came when Sen. John McCain -- despite a down-to-the-last-minute phone call from the President -- refused to get behind the Republican health care bill, effectively sinking it in a vote in the wee hours Friday morning.

While the so-called maverick has long had a reputation for going his own way, his independent style was in hyper drive when he walked onto the Senate floor for the late-night vote on Thursday and gave a blatant thumb down to the bill while standing right before Senate GOP leaders, including McConnell.

His relationship with Trump has long been tense in part because McCain has been unabashed in his criticisms of the president on rhetoric and foreign policy. Most recently -- even as he undergoes treatment for brain cancer -- McCain, who chairs the Senate Armed Services Committee, threatened to provide his own strategy for Afghanistan if the White House doesn't present one soon.

Also beyond health care, Sen. Jeff Flake of Arizona penned perhaps the most scathing rebuke of the President by a Republican yet, with the release of his new book on Tuesday. Flake, who's long been a critic of Trump and who's up for re-election in a heated race next year, argued that Republicans are in "denial" about the President's competence and urged his colleagues in Congress to step up their condemnation of his rhetoric and some of his policies.

The excerpt was published online Monday and quickly reverberated across Washington, though few senators were willing to talk about it the next day. McConnell told reporters he hadn't read Flake's book and refused to comment on the Arizona senator's censure of the President and his own party leaders.

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More unhappiness with Trump

Frustration with Trump is also expressed privately among senators, as evidenced by a recent conversation that accidentally went public. Sen. Susan Collins, another right-of-center Republican who has openly bucked her own party at times, was discussing the president's mental state and competence with Democratic Sen. Jack Reed at a hearing last week while a nearby microphone picked up the conversation.

Reed, as the two were discussing spending measures, said he thought the president was "crazy," and Collins responded with "I'm worried." Collins also expressed doubt that the President was even aware of the Budget Control Act of 2011, which forced stiff spending cuts on defense and domestic programs.

While many of the above-mentioned Republicans have never been considered loyal foot soldiers for the President, the GOP caucus was widely in agreement when senators started pushing back against Trump for attacking Attorney General Jeff Sessions , a former senator himself.

Time after time, Republicans weren't shy in chiding the president in recent weeks for going after the nation's chief law enforcement officer, with some even issuing press releases defending Sessions.

"Jeff Sessions is a man of integrity, loyalty, and extraordinary character," Republican Sen. Richard Shelby of Alabama said in a tweet. "I join the people of Alabama in giving Jeff Sessions my deep respect and unwavering support."

Sen. Thom Tillis, R-North Carolina, also issued a statement defending Sessions last week. When asked by CNN about a potential replacement should Trump fire his attorney general, Tillis expressed concern about the President's leadership style with Cabinet members.

"It raises the question if anyone would want the job," he said.