This much is less ambiguous: Now the committee’s chairman as it investigates ties between President Trump’s associates and Russia, the unobtrusive Mr. Burr is shrugging into a spotlight he never expected and does not especially seem to relish.

The senator’s thorny position — a Republican lawmaker investigating the Republican president, whom he embraced last year on the campaign trail in his own re-election bid — has grown more trying by the day.

Mr. Burr, 61, has watched a fellow Republican, Representative Devin Nunes of California, fumble the House Intelligence Committee inquiry, raising the stakes for a Senate panel that many view as the only credible chance to hold the administration to account on Capitol Hill.

The senator has emerged, whether he likes it or not, as the lawmaker who might well be burdened with undermining not only a president he has supported vocally but the entire G.O.P. in a period of unified rule, championing an inquiry that could consume what was supposed to be a period of conservative policy feats. His supporters insist he is beholden to no one, noting his pledge last year never to seek office again after his re-election.

But at the same time, Mr. Burr’s independence was forcefully questioned after reports in February that he had spoken with the White House and engaged with news organizations to dispute potentially damaging articles about associates of Mr. Trump’s having contact with Russian intelligence operatives. Democrats have grumbled that Mr. Burr was slow-walking his investigation, calling for a special counsel to take up the case.