President Trump walks with Sen. John Barrasso (R-Wyo.), left, and Senate Majority Leader Mitch McConnell (R-Ky.), right, to the Senate Republican Policy Luncheon on Capitol Hill on Tuesday. (Matt McClain/The Washington Post)

President Trump is cajoling Republican senators on the golf course. He is taking Democratic senators for rides on Air Force One. He is calling up fierce critics such as Sen. John McCain (R-Ariz.) to find common cause. He is deploying his daughter and adviser, Ivanka, to pitch activists and swing suburban voters. And he is using his megaphone, Twitter, to boast about it all.

On tax policy, the most consequential legislative fight of his presidency so far, Trump has emerged as a relentless salesman, proclaiming one promise after another. The tax cuts will be "big," he tweets. "Historic." "The biggest TAX CUT in the history of our country."

But for all the bustle emanating from the White House, most of the policy action is at the other end of Pennsylvania Avenue, in the Capitol, as Republicans try to rush through a sweeping tax cut package by the end of the year.

Lawmakers are relying on the president to build public pressure. But on policy details, legislators are focused inwardly as they endeavor to write a bill that could pass the Senate.

Republicans narrowly control the Senate, where some tensions are boiling over tax policy details as well as Trump's leadership in general. In the House, the administration faces other challenges — including that some GOP lawmakers are tuning out Treasury Secretary Steven Mnuchin.

The secretary typically would serve as the administration's chief negotiator on anything related to tax policy. But House Republican leaders have made clear to the White House in recent weeks that they do not want Mnuchin, who has struggled to command respect on Capitol Hill, trying to negotiate with rank-and-file lawmakers, according to three people with direct knowledge of the situation.

National Economic Council Director Gary Cohn is acting as a key interlocutor with Capitol Hill on tax cut legislation. (Jabin Botsford)

National Economic Council Director Gary Cohn — whom Trump considers a master salesman and who gained firsthand experience with corporate tax policy during his years as a Goldman Sachs executive — is serving as a key interlocutor with Capitol Hill, along with White House legislative affairs director Marc Short. White House officials said Mnuchin and Cohn are working in tandem, with the treasury secretary playing a more behind-the-scenes role in shaping the policy and promoting it.

Hungry for a signature piece of legislation to sign, Trump is fully invested in the tax fight, his advisers said.

"President Trump is incredibly engaged and knows this issue really well," said Hope Hicks, the White House director of communications. "To him, it represents so many different tenets of his core campaign promises — job growth, economic development, bringing jobs and money back home from overseas, helping the forgotten men and women."

Trump spends long stretches of his day working in his private dining room, just off the Oval Office, where he sits at the head of a table with a stack of newspapers and a phone beside him. The television often is turned to cable news, and advisers come and go for impromptu huddles. When the topic turns to the tax cut push, which happens more and more these days, Trump sometimes yells to his assistant, Madeleine Westerhout, to get one of the "big six" lawmakers on the phone to talk about his new idea, according to aides.

Ivanka Trump, the president’s daughter and a White House senior adviser, speaks during a town hall meeting on tax reform in Richboro, Pa., on Monday. (Rich Schultz/AP)

But Trump is learning that his willfulness has its limitations, with many other forces within the Republican Party driving the process. As much as the president wants a win, congressional Republicans are asserting themselves as they turn to the details of legislating.

One of the most intense periods in the tax fight will come in early November. Legislators will release the bill, lobbyists will start picking it apart — and Trump will be half a world away, on a 12-day tour of Asia.

Lawmakers seem to be okay with that. Asked if he was concerned that Trump might tweet something that disrupts the carefully planned rollout of the tax legislation, House Speaker Paul D. Ryan (R-Wis.) deadpanned Thursday: "He's going to be in Asia."

Ryan went on to say that he is "working very, very closely with the White House."

But Trump intends to stay involved while overseas, getting regular updates from staff and perhaps tweeting his views. Cohn will stay behind to work with Congress, and Vice President Pence and some Cabinet secretaries plan to do media interviews and hold public events to galvanize support, White House officials said.

It is difficult to overstate the stakes for Republicans. The party has a unified government — controlling both chambers in Congress and the White House — but after a series of defeats is under intense pressure to prove it can govern effectively ahead of the 2018 midterm elections.

"For Republicans, this is existential," said Stephen Moore, a Heritage Foundation economist who advised Trump during last year's campaign.

For Trump specifically, Moore said, "this is the big prize. He's all-in on the tax bill. Having worked with him, I don't think he cares too much about the exact details of this. I think he wants a bill that helps the middle class and cuts the corporate tax. All the rest is just window dressing to him."

David Stockman, who worked as President Ronald Reagan's budget director the last time major tax reform was passed, in 1981, said Trump and congressional Republicans are "barely out of the batter's box."

"Trump is living up to his reputation as the great disrupter," Stockman said. "I don't see the tax bill happening before year end. Even if something passes next year, it will be a pale shadow of what people are talking about and what the market seems to have priced in."

On Wednesday, House Ways and Means Committee Chairman Kevin Brady (R-Tex.) plans to release his draft of the tax cut legislation, holding a committee vote on the measure the following week.

The tax plan is based on several broad ideas, but many provisions remain unresolved. Trump and GOP congressional leaders want to slash the corporate tax rate far below 35 percent and simplify the taxes paid by families and individuals. They want to expand the child tax credit, eliminate the estate tax, and incentivize companies to bring money and jobs back to the United States.

The tax plan would add at least $1.5 trillion to the debt over the next 10 years and, according to numerous budget experts, provide disproportionate benefits to companies and the wealthy. These are just some of the key issues Republicans are trying to address before they bring legislation to the House and the Senate for votes, worried that a few unhappy Republicans could kill the bill.

One of those potential dealbreakers is Rep. Tom MacArthur (R-N.J.), who met with Pence in his West Wing office this week.

MacArthur said in an interview that he tried to convince Pence that the GOP tax plan could drive up taxes for people in his state. Pence heard MacArthur out but was noncommittal, telling him Trump wanted to cut everyone's taxes.

That was not the answer MacArthur was looking for, he said. He wanted substance and a commitment to detailed changes that would help New Jersey. The congressman then voted Thursday to try to block a GOP budget plan in an effort to thwart the entire tax cut push until his concerns were addressed.

He did not succeed.

Asked if the House Republican leaders were sympathetic to the points he tried to make to Pence at the meeting, MacArthur said, "They are only sympathetic to votes."

Many of the decisions about the bill are being made by Brady and his colleagues, which is one reason Pence did not have the power to promise MacArthur that he could make changes.

Mnuchin and Cohn were able to persuade Ryan to back away from a demand that would have included a new way of taxing imports amid concerns that the change could drive up prices on items such as clothing, electronics and automobiles.

But the administration made concessions in other areas. It fell to Mnuchin and Cohn last month to persuade a disappointed Trump to agree to a target for the corporate tax rate that was higher than the president had wanted.

Trump had insisted for more than a year that the corporate tax rate should be lowered from 35 percent to 15 percent, but congressional Republicans stressed that this was not possible, as it would add too much to the debt. Trump ultimately agreed to a rate of 20 percent, which the White House views as an achievement, considering that some House Republicans argued that the rate should be closer to 25 percent.

Still, there are other examples of GOP leaders ignoring some of Trump's demands. The biggest flash point came this week, when Trump announced in a Monday tweet that 401(k) plans would not be affected by the tax bill, apparently reacting to news reports that House Republicans were considering such changes.

White House aides said the president is especially attuned to how the bill will play with middle-class voters and wanted to make clear that he would protect the popular retirement program. But several senior congressional Republican aides said they were rattled by Trump's unexpected declaration. And two days later, Brady told reporters that there still could be changes to these retirement accounts.

Trump has tried to personally win over key Republican senators. He played golf with Sen. Rand Paul (R-Ky.) and Office of Management and Budget Director Mick Mulvaney on Oct. 15 at Trump National Golf Club in Virginia, where the three men chewed over tax policy.

Trump also has golfed several times recently with Sen. Lindsey O. Graham (R-S.C.), who is emerging as a central mediator between the president and Senate Republicans. And Wednesday, Trump called McCain — who earlier this month blasted Trump's "half-baked, spurious nationalism" — to talk about taxes, and the two made plans to get together soon with Graham, according to a White House official.

Ivanka Trump, meanwhile, pitched her child tax credit idea at a town hall meeting in Bucks County, Pa., outside Philadelphia. "It can't just be about cutting taxes," she said.

Ivanka Trump met recently with Grover Norquist, an anti-tax activist with deep influence among Republican lawmakers, to discuss the idea. Norquist said he told her that he respected her efforts but that the plan may not be passable.

"She may not be able to get the size or scope of what she's looking at, but this process isn't about getting everything in this specific bill," Norquist said, recalling how he described his outlook to her. "It takes time, and there will be more than one plane out of Casablanca on taxes."

The president has been trying to woo some Democratic senators to back his tax plan, targeting a handful who are running for reelection next year in states that he won handily.

In late September, Trump invited Sen. Joe Donnelly (D-Ind.) to fly with him to Indianapolis for the president's tax speech. During their conversations on Air Force One, Trump pledged to Donnelly that they could work together on taxes and build a bond, leading the senator to feel cautiously upbeat about the prospect of finding consensus, according to four people familiar with the exchanges.

Donnelly's mood soured, however, once Trump gave his speech at the Indiana State Fairgrounds. The president seemed to threaten the low-key, moderate senator — in front of a large home state crowd — by warning that "we will campaign against him like you wouldn't believe" if Donnelly voted against the tax bill.

White House aides characterized Trump's remarks as well-intentioned, good-natured ribbing, but Donnelly felt burned by the experience and has since had little engagement with the White House, according to the people familiar with the episode.

On Oct. 18, Trump gathered a bipartisan group from the Senate Finance Committee at the White House. With cameras rolling, the president leaned over the dark wooden table in the Cabinet Room to promise the "largest tax cut in the history of our country."

He then joked with Sen. Ron Wyden (Ore.), the committee's ranking Democrat: "I'm sure we'll have unanimous support. I have no doubt, right? Right, Ron? I think. Right?" Senators chuckled.

But once the press corps left the room, there was an immediate disconnect between Trump and some of the Democrats, according to Sen. Robert P. Casey Jr. (D-Pa.).

"I said to him very directly, 'It's good to have this meeting, but I have to tell you, this plan, in my judgment, is a giveaway to the rich,' " Casey recalled in an interview, adding that he rattled off statistics from the nonpartisan Tax Policy Center to make his point.

Casey said he and other Democrats there wanted to make clear to Trump that bipartisan support could not be willed by the president's liveliness. It had to be carefully negotiated, he said.

"But I just don't see it happening," Casey said.

When Sen. Sherrod Brown (D-Ohio) asked Trump to support two of his proposals on how to craft a middle-class tax cut, such as expanding the child tax credit, Trump seemed excited by the idea and said a new set of working groups could be set up.

But later Sen. John Cornyn (R-Tex.) pushed back against Brown's suggestion and said that while he welcomed Democratic input, the committee structure currently in place would drive the talks, according to three people who were briefed on the discussions.

As the meeting wrapped up, Trump vaguely warned that he may hound senators who vote against the bill by visiting their states and rallying against them ahead of the midterm elections.

"He said if those people didn't support a tax cut, it could be pretty tough," recalled Casey, who is up for reelection in 2018. "I'll just say, maybe he was offering a price."