A small group of Republicans may prove a thorn in Donald Trump’s side through the early months of his administration, as he continues to upset conservatives in Congress with his positions on Russia and healthcare.

Senator John McCain, the party’s 2008 nominee for president and a Republican who abandoned Trump late in the 2016 race, has led calls for a congressional investigation into Russian interference in last year’s election.

Citing intelligence chiefs’ conclusions that Russia orchestrated hacks on the Democratic party to sow confusion and help Trump’s candidacy, McCain has insisted he will organize an investigation even if his party’s leaders in the Senate do not join. McCain has also acknowledged that he passed an unsubstantiated dossier, alleging links between the Kremlin and Trump’s campaign, to the FBI last year.

Early in his campaign, Trump ridiculed McCain’s service in the Vietnam war, in which he was captured and tortured by the North Vietnamese. “He’s not a war hero,” Trump said. “He’s a war hero because he was captured? I like people who weren’t captured.”

Trump received five draft deferments from the war.

Senators Lindsey Graham and Marco Rubio have also actively criticized the president-elect’s steadfast interest in making the Russian president, Vladimir Putin, a friend of the Trump White House.

In confirmation hearings, Rubio pressed the question of Putin in sharp questions to Rex Tillerson, Trump’s choice for secretary of state and an Exxon Mobil oil executive who received an “order of friendship” medal from the Russian president.

Tillerson told Rubio he would not use the term “war criminal” to describe Putin over his bombing campaign in Syria, for which the senator scolded him.

“We can’t achieve moral clarity with rhetorical ambiguity,” Rubio said.

Senator Rand Paul, who like Rubio was defeated by Trump in the Republican primary, has suggested he will oppose the president-elect on certain cabinet picks. The libertarian-tinged senator was also the only Senate Republican to vote against a rapid repeal of the Affordable Care Act, Barack Obama’s healthcare reform law.

Paul said he could not reconcile adding $10tn to the deficit with a repeal that fails to account for the budget or adequately replace the system.

Five other Republicans have also resisted the immediate repeal of Obamacare: Susan Collins, Lisa Murkowski, Bob Corker, Bill Cassidy and Rob Portman. The five senators added an amendment this week to give Republicans more time to repeal the ACA and write a replacement.

Representative Charlie Dent, meanwhile, told reporters this week that moderate Republicans in the House similarly have “serious reservations” about acting without a new healthcare plan.

Few Republicans have criticized the president-elect publicly since the election, even though dozens said they would not vote for him after, in October, video was released of Trump bragging about groping women without consent.

On Saturday the Nebraska senator Ben Sasse was one of the few members of his party to defend John Lewis, a Democrat in the House, from Trump’s insult that the civil rights leader was “all talk”.