Kelly faces daunting task of reconnecting Trump to disillusioned GOP establishment Kelly is tasked with getting a chaotic White House back on track.

 -- Among the big challenges that newly minted chief of staff John Kelly faces, repairing relationships in the Republican Party is high on the list.

President Donald Trump’s already tenuous relationship with the party establishment was thrown further into doubt after the ouster of chief of staff Reince Priebus.

Priebus’ presence in the White House was once seen as one of the few tethers binding Trump to the Republican National Committee, as Priebus had the most experience in Washington politics among the president’s senior staff.

Someone who could play peacemaker on Capitol Hill, he utilized his close ties to key Republicans like House Speaker Paul Ryan, but senior White House officials said Priebus’ influence diminished over time in the West Wing.

This is where Kelly comes in: a military man tasked with getting a chaotic White House back on track. He exercised his influence on his first day on the job, with the resignation of White House communications director and Wall Street financier Anthony Scaramucci just days after his hiring.

The resignation came amid concerns over Scaramucci’s addition to the West Wing’s senior staff. He put acrimony and tensions among White House factions on full display last week when he took aim at Priebus and chief strategist Steve Bannon in a foul-mouthed exchange with a reporter from The New Yorker.

Sources in the White House told ABC News that Scaramucci offered his resignation Monday morning to Kelly, with a request to be redeployed as chief strategy officer at the Export-Import Bank, to allow Kelly to assert his leadership in the West Wing.

White House press secretary Sarah Sanders said Monday that Kelly “has the full authority to operate within the White House, and all staff will report to him.”

Though Kelly, a retired Marine Corps general, has little legislative experience, former House Speaker Newt Gingrich is confident Kelly will be able to communicate with members of Congress to effectively push Trump’s legislative agenda.

“He understands the Congress very well,” Gingrich told ABC News, recalling Kelly’s experience as Marine liaison to the House of Representatives in the late 1990s, when Gingrich led the chamber. “Kelly brings order and effectiveness to White House operations ... It is a deliberate change.”

A former Trump campaign adviser describes the current state of the GOP as a problem of elected officials not evolving as Trump has morphed the party.

“The establishment doesn’t have anything to fear from Donald Trump, but they should fear the electorate who doesn’t feel like they’re listening to them,” the former adviser said.

“This is a problem in the White House as well. They need someone who can craft some victories to put two or three wins under our belt,” the former adviser added, describing the current White House legislative strategy as “naive,” unfocused” and “stupid.”

Gingrich predicts the shakeup could spur Trump to reach out more to Democrats, though it's unclear whether any will be receptive.

“Trump will be forced to be more bipartisan for a range of issues, but his base will remain Republican, and the overwhelming bulk of his initiatives will be unacceptable to the left,” Gingrich said.

Deepening the divide between the president and his own party have been his recent attacks on his GOP Senators, with Trump recently calling them “total quitters” if they don’t hold another vote on health care reform. He has even resorted to taunting them, saying, “They look like fools and are just wasting time.”

Vice President Mike Pence, who remains close with many conservative members of Congress, has often had to act as an intermediary between Trump and the Republican establishment — evident most recently in his efforts lobbying House and Senate members on health care. Republicans on Capitol Hill are hopeful that Kelly’s discipline will bring focus to Trump’s legislative agenda.

“Having Gen. Kelly in charge really helps. Focusing on health care,” Sen. Lindsey Graham said on NBC’s “Today” when asked what Trump could do to regain his confidence. “Focus on like a laser on trying to rally the Congress, working with governors of both parties to come up with a new way to deliver health care.”

He added, "Discipline is what I’m looking for.”

In recent months, Trump’s family members, including his sons Donald Trump Jr. and Eric Trump, have met with the Republican National Committee to discuss political strategy.

It’s no question Donald Trump Sr.’s relationship with the RNC has had its share of ups and downs, but the relationship mostly mended after he won the nomination and then the presidency, largely because of the RNC’s ground operation.

It will be a test for Kelly as he seeks to manage the internal crises in the White House while working to assure and maintain support of establishment figures before the 2018 and 2020 elections.