A sense of irritation is setting in among Senate Republicans as President Donald Trump and his close political allies demand more aggressive pushback to the House impeachment investigation.

On Thursday, Senator Lindsey Graham (R-S.C.) introduced a symbolic resolution condemning the Democrats’ impeachment inquiry as inherently unfair and constitutionally problematic. Among other things, the non-binding bill called on the House to hold a vote to open an inquiry, to allow Trump to call witnesses, and to provide congressional Republicans the power to issue subpoenas and “participate fully” in all proceedings.

Graham’s effort was designed as a sop to the president. In fact, the senator had just returned from lunch with Trump at the White House when he introduced his bill, and reported that the president was not at all dissatisfied with the defense he’d received from the Senate GOP.

“I think he feels frustrated that—here we go again,” Graham told The Daily Beast.

But his resolution appeared only to infuriate Trumpworld at large, as it demanded that Senate Republicans hold public hearings and congressional investigations that placed the president’s domestic opponents under the microscope.

“He honestly probably would have been better off doing nothing than that because it’s pretty clear this resolution is nothing more than a ploy to appease the base which is furious at him right now,” said one Trumpworld operative.

That Graham’s maneuver fell short of satisfying the political bloodlust among Trump’s allies didn’t go unnoticed by his colleagues, many of whom have privately griped in recent days about Trump’s eagerness to air his disapproval of the very people he needs in his corner in the event of an impeachment trial. One top GOP Senate operative said that patience on the Hill is “wearing thin.”

“It’s exhausting and they don’t know what they don’t know in terms of where this is going,” the operative added.

Other aides said that they found the attacks from Trump-allied operatives to be counterproductive.

“It’s an interesting strategy,” a senior Senate GOP aide told The Daily Beast, “to attack Republican senators after they try to defend you.”

The friction between Senate Republicans and Trumpworld operatives could complicate an already extremely dicey situation for the White House as it tries to hold party members in line. Publicly, many GOP lawmakers in the Senate remain supportive of the president. But their declarations of support have become notably more cautious and few seemed willing to endorse the idea that they should be using their committees and offices to give Trump more cover.

Sen. James Lankford (R-OK) denounced the Democrats’ impeachment process to The Daily Beast on Thursday, calling it “bizarre” and framing it as unfair to the president. But at this stage, he said, there is a limit to what the Senate can do.

“Ultimately, this is a House issue first,” said Lankford. “We're waiting to see what the House chooses to do.”

Sen. John Kennedy (R-LA), a member of the Judiciary Committee that Graham chairs, is a frequent defender of the president and has attacked the impeachment process. But when asked if the Senate could do more, he said, “It's difficult when you can't see the evidence.” He also backed up Graham in his reluctance to call witnesses at this stage. “We can't, because impeachment starts in the House.”

If Graham were to hold judiciary hearings to interview different witnesses and establish a counter-narrative more favorable to Trump, it’s unlikely that Senate rules and precedent would allow for a process that many Trump backers might want to see.

According to several Senate veterans, the rules of the chamber do dictate that Graham would have to grant Democrats on his committee the chance to call witnesses selected by the minority members of that committee. It is possible, several aides said, that Graham could move to scrap or reset the rules of his committee, though it’s unclear if he’d be successful and doing so would represent a massive breach in norms and risk upending future committee business.

“It’s something we never considered when we were there,” said Greg Nunziata, who was formerly senior Republican counsel on the Senate Judiciary Committee. “The majority and minority historically work in concert in planning hearings. The majority does call the majority of witnesses, but it is practice is to allow the minority to call witnesses as well.”

Graham, on Thursday, said he would not call witnesses to testify, and in doing so he noted that he would have to allow the minority member, Sen. Dianne Feinstein (D-CA), to call witnesses of her own. Graham also admitted that he was under pressure from Republicans to subpoena the Democratic lawmaker running the impeachment probe who is currently Trump’s public enemy number one. “I’m being asked by folks out in the Republican world, why don’t you call Adam Schiff?” Graham said. “I think that’d do a lot of damage to the country, for a senator to call a member of the House.”

While that more measured approach has angered Trump-allied operatives, including the president’s son Don Jr., it is one that has notably been embraced by some in the White House. One senior aide told The Daily Beast that they were waiting to see the results of the U.S. Attorney John Durham’s investigation into the Russia probe origins before deciding on next steps.

“I suppose following his report,” the aide said “further action could be taken as warranted.”

How widely shared this view is inside the White House is not entirely clear. And though Graham told reporters Trump did not evince any dissatisfaction with how Senate Republicans are acting, the president also publicly praised a group of House conservatives for disrupting the impeachment proceedings by literally storming the secured room where depositions are being held. Even some top Trump allies concede that it is a difficult line to walk.

“They are quiet because they tend to be quiet,” Matt Schlapp, head of the American Conservative Union, said of Senate Republicans. “I would say that I do think the Senate has been cautious, but that is the nature of Senate Republicans. They tend to take a lot of time thinking about how to react, and this is just one of those moments where it is a little guttural and the American people want to know where people stand.”