Democrats say there is another reason Republicans favor the Intelligence Committee: Its work is conducted mainly behind closed doors, sparing Mr. Trump and his allies on Capitol Hill from a regular parade of witnesses swearing to tell the truth before sober-faced senators — all of it televised live on cable news and C-Span.

From the McCarthy hearings through Watergate, Iran-contra and the Clinton impeachment, the American public has become quite familiar with the tableaux of the congressional investigation and the serious business that can be involved.

Republicans would like to avoid such a scene to the extent possible. Pursuing an investigation through the Intelligence Committee arms them against complaints that they are looking the other way about the allegations, while potentially limiting the fallout for them and the new administration.

But rapid-fire developments — such as confirmed reports of previously unknown meetings between Mr. Sessions and the Russian ambassador to the United States, Sergey I. Kislyak (meetings he denied at his Senate confirmation hearing), followed by his quick recusal — may erode Republicans’ ability to hold off demands for a wider and more public investigation. Such disclosures have a cumulative effect.

Though most of Mr. Sessions’s former colleagues stood solidly behind him before his recusal announcement, there were prominent cracks. Senator Rob Portman of Ohio, a respected voice among Senate Republicans, issued a statement urging Mr. Sessions to step aside from any Russia-related investigation by the Justice Department. Senator Ben Sasse, Republican of Nebraska, issued his own statement urging the intelligence panel to get on with it.

“Attorney General Sessions’s recusal is the right decision, and the Senate Intelligence Committee should accelerate its work,” Mr. Sasse said, warning that the Russian president, Vladimir V. Putin, was trying to undermine public confidence in American institutions. “The American people deserve a comprehensive, top-to-bottom investigation of Putin’s Soviet-style meddling in self-government at home and across the West.”

Their positions, and more private expressions of increasing nervousness by other lawmakers, show that Republican unity on how to respond to Russia’s meddling in the election is not a given, and that further disclosures could bring about more defections from the party line that no investigation beyond the intelligence community is warranted.