“Recent reports of Russian interference in our election should alarm every American,” the four senators said in a statement on Sunday morning. “Democrats and Republicans must work together, and across the jurisdictional lines of the Congress, to examine these recent incidents thoroughly and devise comprehensive solutions to deter and defend against further cyberattacks.”

“This cannot become a partisan issue. The stakes are too high for our country. We are committed to working in this bipartisan manner, and we will seek to unify our colleagues around the goal of investigating and stopping the grave threats that cyberattacks conducted by foreign governments pose to our national security,” they added.

But McCain and Graham — who frequently criticized Trump before and after his election — have often bucked Republican leaders, and their embrace of a wide-ranging Russia probe does not necessarily signal support from other Republicans, including Senate Majority Leader Mitch McConnell (R-Ky.).

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Sen. Susan Collins (Maine), one of the more moderate Republicans in the upper chamber, suggested a bipartisan investigation may be “useful toward achieving an objective accounting of any alleged meddling by foreign adversaries.”

“The purpose of any investigation, whether by the Obama administration or Congress, is not to question or relitigate the results of any past or present Presidential election,” she said in a statement. “Instead, any review must focus on the long overdue task of improving the defenses of the United States against cyber attacks, including those that might seek to affect or influence political campaign.”

Another GOP senator — Sen. James Lankford (Okla.), who serves on the Senate Intelligence Committee — agreed with McCain and Graham’s decision to support a bipartisan investigation of suspected cyber intrusion by Russia in the U.S. elections.

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“Cybersecurity investigation of Russian interference can’t be partisan,” Lankford tweeted Sunday.

Meanwhile, the Senate Intelligence Committee’s chairman, Richard Burr (R-N.C.), said Sunday that the panel “will continue to conduct vigorous oversight of all intelligence matters.”

But he made no specific mention of Russia, unlike Sen. Ron Johnson (R-Wis.) said cyber threats by America’s “rivals,” including Russia, pose “serious challenges” that should not be “politicized or viewed through a partisan lens.”

Johnson said as chairman Senate Homeland Security and Governmental Affairs Committee and a member of the Senate Foreign Relations panel he would “continue to hold hearings based on fact — not innuendo — for the sole purpose of informing effective policy and appropriate countermeasures.”

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Republicans may be loath to join calls for such a wide-ranging investigation into Russia’s election-related activities given that Trump has dismissed the CIA claims as “ridiculous.” They may worry about picking an obvious fight with the president-elect before he is even inaugurated. Trump has signaled he wants a warmer relationship with Russian President Vladimir Putin, whom he praised during the campaign.

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“I think it’s just another excuse. I don’t believe it . . . No, I don’t believe it at all,” Trump said of the CIA charges on “Fox News Sunday.” Trump campaign manager Kellyanne Conway echoed her boss on CBS’s “Face the Nation,” saying that such allegations from the intelligence community were “laughable and ridiculous.”

Trump also played down the importance of receiving the daily intelligence briefing, a tradition for presidents and presidents-elect. He has received the briefings only sporadically since winning the election.

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A U.S. intelligence official said it is “concerning” that intelligence on Russia relating to the election is “being dismissed out of hand as false or politically partisan.” “The inclination to ignore such intelligence and impugn the integrity of U.S. intelligence officials is contrary to all that is sacred to national security professionals who work day and night to protect this country,” said the official, who spoke on the condition of anonymity because of the sensitivity of the issue.

McConnell himself has been notably silent since the Post report was published on Friday night, and his number-two, Senate Majority Whip John Cornyn (R-Texas), downplayed the significance of it in a series of tweets — although some of them suggested Congress’s review of Russian actions should broaden.

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“All this ‘news’ of Russian hacking: it has been going on for years. Serious, but hardly news,” Cornyn tweeted Saturday.

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The Texas Republican seemed to support, however, a wider look at Russia as a global actor rather than one confined to its role in the U.S. election, retweeting the below tweet from Graham:

“Cyber-attacks, undermining NATO, Ukraine, butchery in Syria, etc. I intend to look at all things Russia – not just election influence.” https://twitter.com/JohnCornyn/status/807629913792647168

Meanwhile, House Speaker Paul D. Ryan (R-Wis.), in his first substantial comment on Russian hacking since the report Friday, said Sunday he “rejects any politicization of intelligence matters,” calling foreign intervention “unacceptable.”

For the most part, other key Republicans were silent on the issue of whether to embrace a bipartisan look at whether Putin’s government was behind the hacks of the Democratic National Committee emails and their publication by WikiLeaks in an alleged bid to help Trump and damage Hillary Clinton’s campaign.

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At the same time, several Republican senators raised concerns about Trump’s likely nomination of Rex Tillerson, ExxonMobil’s chief executive, as secretary of state due to his ties to Putin. Republicans in a 52-to-48 Senate have only the slimmest of margins to get him confirmed, should Democrats decide to uniformly oppose the nomination. Only three Republicans would need to side with Democrats in order to defeat Tillerson.

The potential nomination sparked a backlash among the party’s traditional hawks who oppose Putin, and some senior strategists feared that more than a handful of Republicans would outright oppose his nomination – requiring Trump to find Democratic support in order to confirm his potential Secretary of State.

“It’s a matter of concern to me that he has such a close relationship with Vladimir Putin, that that would color his approach to Vladimir Putin and the Russian threat,” McCain told CBS’s Face the Nation.

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“Being a ‘friend of Vladimir’ is not an attribute I am hoping for from a Secretary of State,” Sen. Marco Rubio (R-Fla.) tweeted Sunday. Republicans outnumber Democrats by only one vote on the Senate Foreign Relations Committee, which must approve a secretary of state nominee before the full Senate votes.

Over the weekend, several committee Democrats, including Sens. Robert Menendez (N.J.) and Christopher A. Coons (Del.), stated their deep skepticism of Tillerson as a candidate. In a post on Facebook, Menendez called the idea Tillerson could be named secretary of state “alarming and absurd,” concluding that “the Trump administration would be guaranteeing Russia has a willing accomplice in the President’s Cabinet guiding our nation’s foreign policy.”

Yet the committee’s chairman, Sen. Bob Corker (R-Tenn.) — who was considered a possible pick for Trump’s secretary of state — has said Tillerson would be a good choice. “If it is Rex Tillerson, he is a very impressive individual,” Corker tweeted. Should Tillerson make it to a floor vote, Democrats could not block the nomination alone.

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If Democrats stick together, Republicans must muster at least 50 of the 52 votes they will have to successfully confirm him, as Vice President-elect Mike Pence could cast the tiebreaking vote. Graham has already also strongly hinted that he might oppose the nomination.

“I don’t know the man much at all, but let’s put it this way: If you received an award from the Kremlin, order of friendship, then we’re gonna have some talkin’,” Graham said early Saturday morning. “We’ll have some questions. I don’t want to prejudge the guy but that’s a bit unnerving.”