(CNN) The party of Reagan is fast lurching into a mini-Cold War with itself -- this time over working with Russia rather than against it.

President-elect Donald Trump's affinity for Russian President Vladimir Putin and his denials that the Kremlin hacked the 2016 election are unleashing a feud in the GOP, which sees its hawkish history on Moscow and triumph over the Soviet Union as one of its defining achievements.

The turmoil is threatening to detract from one of the most crucial moments of Trump's early presidency -- the confirmation process for his nominee for Secretary of State Rex Tillerson, who has a personal friendship with Putin and opposed US sanctions on Russia imposed after the Kremlin's annexation of Crimea.

The idea that Russia may not pay a price for the startling allegation of seeking to undermine American democracy with a series of cyber breaches is infuriating some senior Republicans, and putting even those less hostile to Trump in a tough political spot.

"I can't imagine I would vote for anybody that believes that we should not sanction Russia, given the fact that they did in fact interfere in our election," South Carolina Republican Sen. Lindsey Graham told CNN's Wolf Blitzer on the "Situation Room" on Wednesday.

Deepening Washington showdown

The Washington showdown over how to combat Russian interference in the election is also testing the uneasy truce that has prevailed between the White House and the Trump operation since November.

And it is a sign of the unusual intra-party dilemmas beginning to unfold in Washington rooted in the next president's unorthodox approach to policy and wielding power.

With the intrigue deepening by the hour over what intelligence agencies, the White House and top figures on Capitol Hill now agree was a Russian effort to intervene in the election, Trump weighed in with a reminder that he is not on board with this consensus.

"If Russia, or some other entity, was hacking, why did the White House wait so long to act? Why did they only complain after Hillary lost?" Trump told his 17 million Twitter followers on Thursday.

If Russia, or some other entity, was hacking, why did the White House wait so long to act? Why did they only complain after Hillary lost? — Donald J. Trump (@realDonaldTrump) December 15, 2016

Trump's comment that the administration waited until after Democrat Hillary Clinton was defeated in the election is not accurate. The alleged hacking was a topic in the presidential campaign as early as July and surfaced in the debates. In October, US covert agencies issued a statement alleging Russia itself was behind the hacks of the American political system.

But in a Fox News Sunday interview over the weekend, the President-elect suggested that there was no proof Russia had hacked the election, saying the Russian snooping in Democratic Party servers and emails of Clinton campaign staffers could have been done by China or even someone sitting in New Jersey.

Trump's stand means that an incoming president is directly at odds with his own intelligence agencies and the assessment of the entire Washington establishment.

Following Trump's tweet Thursday, there was one sign that his camp recognized the loneliness of his position.

A transition source said the President-elect was "concerned" about the Intelligence Community's findings that Russia hacked the election.

But the source also said Trump and his team are concerned the issue is being used to delegitimize his victory. Trump aides have consistently accused the Democrats and critics of Trump in the CIA of drumming up the hacking issue to undermine his victory in November.

Tillerson in trouble?

Unless there is an evolution in the nascent administration's position on Russia, especially over sanctions, there could be trouble for Tillerson.

Only a few Republican senators would need to defect for his nomination to be in jeopardy, assuming most Democrats in the chamber -- where the GOP has a 52-48 majority -- vote against him.

The salience of the sanction issue for Republicans shows there's a depth of resistance to a reorientation in US policy toward Russia that goes beyond the hacking issue.

Graham made that point clear in his skepticism about Tillerson.

"If (someone doesn't) believe sanctions are appropriate, given what Putin has been doing all over the world, including in our backyard, then I don't think they have the judgment to be secretary of state," Graham said.

"Because if you don't go after Russia, you're inviting the other bad actors on the planet to come after you."

GOP heavy hitters, including Florida Sen. Marco Rubio and Arizona Sen. John McCain, have also raised concerns about the relationship Tillerson forged with Putin and his top aides while heading ExxonMobil.

The possibility that Trump could consider lifting US sanctions on Russian entities and officials imposed to punish the annexation of Crimea gained credibility after a former campaign surrogate showed up in Moscow this week to brief US business people.

"Trump can look at sanctions. They've been in place long enough," Jack Kingston said during an interview with NPR in the Russian capital."Has the desired result been reached? He doesn't have to abide by the Obama foreign policy. That gives him a fresh start."

The former Georgia congressman told NPR he did not have any meetings with Russian officials.

Another Trump adviser, Walid Phares, told Middle Eastern diplomats on Wednesday that the President-elect's bid to improve relations with Russia would help boost administration priorities in the region, including ending the war in Syria.

The possibility that such an approach could align Washington alongside Moscow and Syrian President Bashar al-Assad, who is blamed for much of the slaughter in the war, is likely to alarm the same Republican critics who worry about Trump's emerging Russia policy.

Still, it is far from clear exactly how Trump's Russia policy will unfold. While foreign policy observers have deduced he will try to forge a working relationship with Putin -- of whom he spoke admiringly on the campaign trail -- Trump's exact conditions for a rapprochement are unknown.

There are many intangibles bound up in whether the two presidents actually make a personal connection, as they have not previously interacted. It's also possible that the new US leader may not take kindly to the Russian leader should he attempt to manipulate him -- or that their relationship could sour over time, an experience common to Trump's predecessors President George W. Bush and President Barack Obama.

And it remains unclear if Tillerson's relationships will remain as cordial when he is pursing America's interests with Russia rather than ExxonMobil's.

They are questions that will feature prominently in his confirmation hearings.

Some in GOP want better Russia ties

While there is angst among some Republicans over Russia policy, there are others willing to offer Trump the benefit of the doubt.

Former Obama Defense Secretary and Republican Sen. Chuck Hagel told CNN on Thursday that he was "encouraged" that there would be an effort to ease US-Russian tensions in the new administration.

"I am encouraged by that," Hagel said, "but that doesn't discount or at all put aside the big differences we have with Russia," in particular in Syria and Ukraine.

But he added: "We have got to find some platforms of stability to start working together if we can. Can they find enough common ground? We will see."

Trump's intentions toward Russia will become clearer once he has a full foreign policy team in place.

In the meantime, the controversy over the Russian intelligence operation is straining the fragile detente between Obama's White House and the Trump transition effort.

White House spokesman Josh Earnest took exception on Thursday to Trump's attitude, recalling that the President-elect's campaign team had described his call on Russia to hack Clinton's email server over the summer as a joke.

"I don't think anybody at the White House thinks it's funny that an adversary of the United States engaged in malicious cyber activity to destabilize our democracy," Earnest said on Thursday.

And Earnest, presumably reflected increasing impatience with Trump among senior officials in the White House, also rebuked him for his refusal to accept that Russia was behind election meddling.

"It might be time to not attack the intelligence community but to actually be supportive of a thorough, transparent, rigorous, nonpolitical investigation into what exactly happened," he said.