President Trump and high-level administration officials are using a lighter touch to help the Republican healthcare bill through the Senate as compared with the House, putting tremendous pressure on Senate Majority Leader Mitch McConnell as skeptical GOP lawmakers threaten to defect on a key procedural vote this week.

"Sink or swim, this bill rests on the shoulders of leadership," one GOP Senate aide told the Washington Examiner. "It is their product with minimal White House involvement."

The White House has publicly backed the bill and expressed optimism that an Obamacare overhaul could advance before lawmakers leave for the July 4 recess at the end of the week. But privately, the president and his team have left much of the heavy lifting to McConnell, who faces the challenge of changing the legislation to satisfy some or all of the five Republican senators who oppose it as it is written.

Trump picked up the phone over the weekend to call four Republican senators who have expressed concerns about the healthcare plan: Ted Cruz of Texas, Rand Paul of Kentucky, Shelley Moore Capito of West Virginia and Ron Johnson of Wisconsin. And, on Friday, Vice President Mike Pence called Sen. Dean Heller after the Nevada Republican came out strongly against the bill, a White House aide told the Washington Examiner.

Overall, however, congressional aides say the administration's efforts have fallen short of the full-court press it launched in favor of the House's healthcare legislation earlier this year.

Trump, Pence and a number of top White House aides worked aggressively to build support for the House version of the Obamacare replacement bill in April and early May. Trump personally journeyed to Capitol Hill, invited members to a bowling night at the White House, hosted a series of meetings in the Oval Office and lit up the phone lines selling legislation he has since described as "mean."

White House chief of staff Reince Priebus and chief strategist Steve Bannon made multiple trips to the halls of Congress as well, appealing directly to the House members who had reservations about the healthcare bill. Pence and budget director Mick Mulvaney were especially involved in negotiations with the Freedom Caucus and other conservative lawmakers.

Trump celebrated with House Republicans in the Rose Garden when the bill passed the lower chamber. "This has really brought the Republican Party together, as much as we've come up with a really incredible healthcare plan," the president said at the time. "This has brought the Republican Party together."

The Senate, however, presents the administration with a different set of challenges. Individual senators wield far more influence over the future of the bill than individual House members, and those who have announced opposition to the legislation already have clear ideas about what changes could earn their support. In the House, on the other hand, Pence and other administration officials made inroads by facilitating talks between larger groups of members, such as the Freedom Caucus and the centrist Tuesday Group.

Pence will be back on Capitol Hill Tuesday for the weekly Senate Republican lunch, where he will likely discuss the perilous path forward for the Obamacare reform bill.

"He'll have a few meetings with individual lawmakers while he's on the Hill," said an aide to the vice president. "He continues to take calls, and he'll have meetings."

Later Tuesday evening, Pence has invited a handful of Republican senators — including Utah Sen. Mike Lee, who opposes the bill in its current form — to a dinner at his home, the Washington Examiner confirmed.

Senate Republicans tweaked their bill Monday as its fortunes grew dimmer ahead of a procedural vote that will determine whether the legislation will even come up for debate on the floor. They added a provision to punish individuals who allow their coverage to lapse for an extended period of time in an effort to stabilize the insurance market under the Obamacare repeal plan. But Republican senators have requested more changes to the legislation, and the White House said Monday that Trump would welcome additional fixes.

"He'll continue to support ways to make the bill stronger," White House press secretary Sean Spicer said of Trump's involvement with the healthcare plan.

A group created to promote the president's policies has taken a far less nuanced approach to the legislation. America First Policies, sanctioned by the president and staffed by a number of former Trump campaign and West Wing aides, pursued a seven-figure advertising campaign in Nevada on Monday to highlight Heller's opposition to the bill and bought ads in the home states of several other senators who say they plan to vote against it. The move could complicate the relationship between GOP lawmakers and Trump as administration officials work to help Senate leaders scrape together the votes necessary to repeal Obamacare.