Standing aside President Donald Trump on Monday night, Sen. Rand Paul called for the media to unmask the Ukraine whistleblower and was cheered by rallygoers in Kentucky.

“Do your job and print his name!” Paul said as the president clapped and looked on approvingly.

But on Tuesday morning, some of Paul’s colleagues were cool to the idea of exposing the identity of the person who helped launch the impeachment drive by detailing Trump’s call with the Ukrainian president.

Senior Senate Republicans are worried about the precedent it would set, fearing government sources would be less likely to reveal wrongdoing in future presidencies.

They also have a simpler concern: Not breaking the law.

“We should follow the law. And I believe the law protects whistleblowers,” said Sen. Lamar Alexander (R-Tenn.).

“The whistleblower statute is there for a reason. And I think we need to respect the law where whistleblowers are concerned. Eventually that person may decide to come forward voluntarily,” said Senate Majority Whip John Thune (R-S.D.), who added that senators like Paul are frustrated with the lack of transparency from the House.

Sen. Rob Portman (R-Ohio) said officials “ought to respect the whistleblower laws,” as did Sen. Rick Scott (R-Fla.). Several senators cited the work of Chuck Grassley, the most senior Senate Republican, who has made whistleblower protections a signature issue.

On Tuesday the Iowa Republican reiterated his stance. “All I can say is I expect whistleblowers to be protected according to what the law gives them,” Grassley said.

“I write whistleblower laws, I gotta go by what the law says, and things of that nature so I made my position pretty clear,” he added. “And journalists will have to do what journalists do.”

Sen. Mitt Romney (R-Utah) also expressed his support for the whistleblower.

“Whistleblowers should be entitled to confidentially and privacy, because they play a vital function in our democracy,” Romney said.

Not everyone is breaking with Paul, a libertarian-leaning Republican whose positions are often at odds with his colleagues.

Sen. Lindsey Graham (R-S.C.), who is also tight with Trump, said the public should “absolutely” know the whistleblower’s identity and argued the whistleblower statute is being “terribly abused.”

“I don’t think the president of the United States needs to be impeached based on an anonymous complaint,” Graham said. “There is no substitute for us knowing who the whistleblower is. What connections does he have to other people? What are the biases, if any? You cannot do this without the whistleblower being cross-examined.”

Sen. John Barrasso (R-Wyo.) said Tuesday that whistleblowers should be able to come forward but added — in an echo of Trump and his allies — “people ought to be able to face their accusers.”

The president has aimed sustained attacks on the whistleblower and several conservative media outlets have speculated on the person’s identity, leading Paul to call for more mainstream outlets to join the effort. Trump himself has encouraged the media to reveal the whistleblower’s identity.

In such a politically-charged atmosphere, several GOP senators declined to answer the questions. Others said that the whistleblower complaint has been overtaken by other events.

“It’s kind of a moot issue. … People can read the transcript themselves,” said Sen. John Cornyn (R-Texas).

“He’s already been outed. I think we all know who it is,” said Sen. Joni Ernst (R-Iowa) cryptically.

The Senate Intelligence Committee is also interested in the whistleblower, according to Sen. Roy Blunt (R-Mo.), a member of the committee.

Blunt said that he did not share Paul's view that the whistleblower's identity should be made public “but it's also not my view that the whistleblower should be able to answer questions anonymously.”

“The whistleblower should come and answer questions for the Intel Committee,” Blunt said.

A spokeswoman for Chairman Richard Burr (R-N.C.) confirmed that Burr wants to interview the whistleblower.

Even as Republicans debated the notion of unmasking a confidential government source protected by whistleblower law, a new litmus test was already emerging for the party.

On Monday, Paul tweeted that both the whistleblower and Hunter Biden should be subpoenaed by Congress — leading to a new round of questions for members of the GOP.

Cornyn said the former vice president’s son could be called to testify “If there’s legitimate legislative interest in doing so. Otherwise I wouldn’t do it.”

James Arkin contributed to this report.