(CNN) Donald Trump Jr. is balking at answering more questions about the June 2016 Trump Tower meeting and the pursuit of a Trump Tower Moscow project, two sources familiar with the matter told CNN, setting the stage for a clash with the Republican-led committee amid pressure from both parties over the subpoena to President Donald Trump's eldest son.

Senate Intelligence Chairman Richard Burr, who signed off on the subpoena to Trump Jr. , told his colleagues that the panel has been engaged in talks with Trump Jr. since last December, and that he had agreed to voluntarily be interviewed on two separate occasions before backing off, according to sources familiar with the matter. That move prompted Burr and Democratic Sen. Mark Warner to ultimately issue the subpoena for his testimony, after Trump Jr.'s legal team objected to the scope and breadth of the planned interview, according to one source.

But with Trump Jr. and his allies now mounting a fierce pushback against Burr, the GOP chairman could soon be forced to make a difficult decision if Trump Jr. defies the subpoena: whether to hold Trump Jr. in contempt and risk further GOP backlash or give the President's eldest son a pass and spark outcries of favoritism.

The two sides have had discussions since news of the subpoena broke last week, though it remains unclear if a deal can be reached. One person familiar with the discussions said it's possible Trump Jr. could agree to provide written answers, short of returning to testify in person, although the committee has previously rejected receiving written responses from Trump Jr.

Trump Jr.'s approach to the interview appears to have rankled the powerful Republican committee chairman, leading to the tense stand-off pitting Burr and Warner against the President's son and his Republican allies. The dispute is all the more remarkable given that Burr, a Republican, was first to issue a subpoena to a member of the President's family amid the House Democrats' war with the White House over their investigations into Trump's administration, businesses and finances.

Sources with knowledge of the discussions told CNN the committee initially provided Trump Jr. with a list of roughly a dozen topics that investigators want to cover, including the Trump Tower meeting and Trump Tower Moscow. Trump Jr.'s legal team expected a much shorter followup interview than proposed by the committee, which would not agree to limit the time or topics, according to the sources.

But Trump Jr.'s lawyers are pushing back at addressing questions about the June 2016 meeting or Moscow project because he's already sat before three congressional committees for more than 20 hours and answered questions about those topics under oath, the people said. Trump's lawyers viewed the format of the followup interview as effectively a "do-over" from his 2017 appearance.

There is a concern, echoed by several Republicans, that the interview is an effort to try to catch Trump Jr. in a lie since several Democrats have already accused Trump Jr. of committing perjury, the sources said.

Trump Jr.'s lawyers have argued that both the Trump Tower Moscow project and the Trump Tower meeting are detailed in special counsel Robert Mueller's report, although Trump Jr. declined to speak to the special counsel's office.

Still, the panel wants to clear up potential discrepancies from his past testimony about the Russia project and the June 2016 meeting.

A lawyer for Trump Jr. declined to comment for this story, as did a spokeswoman for Burr.

The committee is now at a standoff with Trump Jr. over the subpoena, while Trump Jr.'s Republican allies ratchet up pressure on Burr to drop the matter and Democrats demand punitive measures against Trump Jr.

While the subpoena was only revealed last week, the negotiations have been ongoing for several months, before Mueller finished his investigation. After the news broke, Burr kept quiet publicly but defended the move in private discussions with his colleagues, telling GOP senators about the months-long negotiations to secure his return, according to a source briefed on the comments.

After noting that the President's son agreed to come in on two different dates, then backed off, Burr explained that when Trump Jr.'s team postponed a planned April 4 interview, the committee said he could no longer delay his appearance. The panel gave him until April 8 to reconsider, at which point it issued the subpoena, according to the source.

Senate Majority Leader Mitch McConnell has not publicly taken issue with Burr amid the dispute. McConnell's office was made aware of the subpoena at least a week before it was publicly disclosed, but deferred concerns raised to the committee, according to a source familiar with the discussions.

Pressure mounts on Burr

The subpoena has sparked a sharp backlash from Trump Jr.'s Republican allies — including many of Burr's Senate colleagues — publicly urging Burr to drop the matter and questioning his decision.

Trump, who said last week he was "very surprised" at the subpoena from Burr, tweeted a story Sunday about the Republican pressure on Burr and added: "Really sad!"

Senate Judiciary Chairman Lindsey Graham, who is up for reelection in 2020, told Fox News it was time to "call it a day," specifically questioning any reliance on former Trump personal lawyer Michael Cohen's testimony.

"If I were Donald Trump Jr.'s lawyer, I would tell him, you don't need to go back into this environment anymore," Graham said. "You have been there for hours and hours and hours, and nothing being alleged here changes the outcome of the Mueller investigation."

On Monday, Graham suggested that Trump Jr. should invoke his Fifth Amendment rights to avoid answering questions.

"If I were his lawyer, I would just take the Fifth and be done with it," Graham said.

The former Senate Judiciary Chairman, Sen. Chuck Grassley of Iowa, declined to answer questions Monday about whether Trump Jr. should comply with the Intelligence Committee's subpoena.

"I don't have an answer for you," Grassley said. "Because for me to answer your question, I would have to divulge information I got in the caucus, that they asked us to keep private because everything that goes on in that committee is tightly held."

The Republican criticism is forcing Burr into a spotlight he's tried to avoid throughout much of the panel's two-year investigation into Russian election interference.

"I think the outcry from most of the people in North Carolina has been one of surprise -- and certainly not supportive," Rep. Mark Meadows, a fellow North Carolina Republican, told CNN about the subpoena. "If there's one thing that I do hear from North Carolina voters it's: 'It's time to move on.'"

Before the blowup over Trump Jr., Burr had earned praise in the Senate for the bipartisan handling of the probe, which moved forward quietly with a stream of witnesses moving before the committee.

Burr made a point of rarely attending White House events or speaking with the President. It's also not clear whether Burr will be swayed by the political pressure, given that he's already said he's not planning to run for reelection when his term ends up 2022, freeing him of concerns about a primary challenge.

And earlier this year, Trump was cheering Burr on after the North Carolina Republican said his investigation had found no evidence of collusion, a comment that earned a rare public disagreement from Warner.

Questions over Trump Jr.'s testimony

Trump Jr. testified in 2017 before three committees — Senate Intelligence, House Intelligence and Senate Judiciary — amid the uproar over the June 2016 Trump Tower meeting in which Trump Jr. was promised dirt on Hillary Clinton.

The Senate Judiciary Committee has released a transcript of his testimony, which has been questioned in the wake of the Mueller report about both the Trump Tower meeting and the Trump Tower Moscow project.

Trump Jr. told the Senate panel that he had only told campaign chairman Paul Manafort and Trump's son-in-law Jared Kushner about the Trump Tower meeting ahead of time. But then-Trump campaign deputy Rick Gates, who pleaded guilty in the special counsel probe, told Mueller's team that Trump Jr. said he had a lead on negative information about the Clinton Foundation at a morning campaign meeting in the days before the Trump Tower meeting.

Trump Jr.'s testimony on the Trump Organization's Trump Tower Moscow project has also come into question.

Trump Jr. told the Senate Judiciary Committee he was "peripherally aware" of the project, but Mueller's report says that Cohen testified he had discussed the project on multiple occasions with Trump Jr. and that was not "idle chit chat."

Some Democrats have called for the committee to take action over Trump Jr.'s refusal to appear — Sen. Richard Blumenthal of Connecticut said Trump Jr. should be jailed — but the committee's top Democrat has defended Burr's handling of the situation.

"He's been under enormous pressure at times from certain members to shut down the investigation, I've been under pressure to reach a conclusion before we're finished," Warner said. "I think we've resisted that, and I think as you see the work product of this committee, the committee will be proud, and candidly the American public will get to see how the Congress is supposed to work."