[Update: At a late afternoon press conference Attorney General Sessions agreed to recuse himself from any investigation into Russian involvement in the 2016 US presidential election.]

Russia is becoming the scandal the Trump administration just can’t shake.

A steady drip of revelations regarding the Trump team’s communications with Russian officials is dismaying congressional Republicans as well as Democrats, leading to calls for a more intensive investigation into the circumstances and substance of these connections.

In particular, many lawmakers were surprised on Wednesday night by a report in The Washington Post that Attorney General Jeff Sessions had twice spoken with the Russian ambassador during the presidential campaign. In sworn testimony during his confirmation hearing, Mr. Sessions had appeared to say that no such conversations took place.

Some GOP members are now joining Democratic members in calling for Sessions to step aside from an investigation into Russian interference in the election, or even appoint a special prosecutor for an independent effort. Such a probe could distract and dispirit the White House for months, as Benghazi and Iran-Contra investigations did for other administrations in different times and circumstances.

“I think it’d be easier” for Sessions to step back from titular oversight of the Russia investigations, House majority leader Kevin McCarthy (R) of California said on Thursday, before walking the remarks back a short time later.

The congressional GOP is not backing away from support of Sessions en masse. As of Thursday afternoon, Rep. Jason Chaffetz (R) of Utah, chairman of the House Oversight Committee, is the top-ranking House member calling for recusal. At least two GOP senators – Lindsey Graham of South Carolina and Rob Portman of Ohio – were taking that position as well.

But others may follow. Perhaps as notable as those speaking up were those staying silent. There seemed little overt support for Sessions, though House Speaker Paul Ryan said that the attorney general should not step down unless he himself was the focus of the executive branch Russia investigations.

The stream of news reports may be taking its toll on the GOP, the bulwark of Trump’s support on Capitol Hill. The Post’s story about Sessions was not even the only big story on the subject released Wednesday: The New York Times reported that, in their last days in office, some Obama officials scrambled to ensure that intelligence regarding contacts between Trump team members and Russian officials was preserved and spread throughout the government, so as to be easier for investigators to find.

No one in Congress wants to take a stand on the Russia question, then be disproved by later events. After all, former national security adviser Michael Flynn initially denied contacts with the Russian ambassador prior to the election. That turned out to be untrue and he was forced to resign.

As to Sessions’ situation, “I think he should recuse himself. More importantly, he needs to explain the context those meetings [with the Russian ambassador] took place in,” says James Kirchick, a fellow with the Foreign Policy Initiative and author of the forthcoming book “The End of Europe: Dictators, Demagogues, and the Coming Dark Age.”

Calls for Sessions’ resignation are a bit overblown, according to Mr. Kirchick, but an independent prosecutor might be appropriate for the situation. That’s something the Trump administration has vehemently opposed. But as long as they do, there may be suspicions about their actions and motives, given the amount of smoke in the air on the subject.

Sessions was a member of the Senate Armed Services Committee at the time of his meetings with Russian Ambassador Sergey Kislyak. They were brief and their contents might well have seemed innocuous. But Ambassador Kislyak’s intentions might have been more nuanced. He could well have been simply cultivating someone who promised to be an entrance into a Trump campaign whose ideological inclinations seemed promising to the Kremlin.

“That’s part of a broader story – this is a culmination of a longtime Russian strategy of cultivating [nationalist] right movements around the world. It’s the opposite of the cold war, when they cultivated the left. Now Russia is more a reactionary power,” says Kirchick.

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For Trump administration officials, their deepening Russia problems are a frustration at best. Many of their attempts to get past the controversy end up feeding it – witness their attempt to enlist the FBI to knock down a previous New York Times story about administration/Russia connections. That only produced more headlines on the subject.

In that context, an independent prosecutor could turn the probe into something analogous to Benghazi – much more difficult for the subject of the investigation to limit in time or subject. Remember that the Benghazi inquiry, ostensibly about a 2012 tragedy at a US outpost in Libya, turned up evidence that then-Secretary of State Hillary Clinton conducted government business on a private email service.