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Mr. Trump and his staff played a critical role in persuading House Republicans to pass health care legislation in May, with the president personally calling dozens of wavering House members. But the Trump teams heavy-handed tactics have been ineffective in the Senate, and White House officials determined that deploying Vice President Mike Pence, a former congressman with deep ties to many in the Senate, was a better bet than unleashing Mr. Trump on the half-dozen Republicans who will determine the fate of the Senate bill to repeal and replace the Affordable Care Act.

Mr. Trump, who is fond of telling friends he is a closer, became more involved over the past few days, reaching out to a few reluctant conservatives like Senators Mike Lee of Utah, Ted Cruz of Texas and Rand Paul of Kentucky, who emerged from an Oval Office meeting on Monday saying he was more optimistic about getting to a yes.

The White House has been very involved in these discussions, Mr. McConnell said in announcing that a vote on the bill was postponed until after the Fourth of July recess. Theyre very anxious to help.

Yet over the past few weeks, the Senate Republican leadership has made it known that it would much rather negotiate with Mr. Pence than a president whose candidacy many did not even take seriously during the 2016 primaries. And some of the White Houses efforts have clearly been counterproductive.

Over the weekend, Mr. McConnell made clear his unhappiness to the White House after a super PAC aligned with Mr. Trump started an ad campaign against Senator Dean Heller, Republican of Nevada, after he said last week that he opposed the health care bill.

The majority leader already rankled by Mr. Trumps tweets goading him to change Senate rules to scuttle Democratic filibusters called the White House chief of staff, Reince Priebus, to complain that the attacks were beyond stupid, according to two Republicans with knowledge of the tense exchange.

Mr. McConnell, who has been toiling for weeks, mostly in private, to put together a measure that would satisfy hard-liners and moderates, told Mr. Priebus in his call that the assault by the group, America First, not only jeopardized the bills prospects but also imperiled Mr. Hellers already difficult path to re-election.

Mr. McConnell and several other Republican senators expressed their irritation about the anti-Heller campaign during the White House meeting, according to two people, one of them a senator, who were present.

The move against Mr. Heller had the blessing of the White House, according to an official with America First, because Mr. Trumps allies were furious that the senator would side with Nevadas governor, Brian Sandoval, a Republican who accepted the Medicaid expansion under the health law and opposes the Republican overhaul, in criticizing the bill.

According to the senator, the president laughed good-naturedly at the complaint and signaled that he had received the message.

A few hours later, America First announced it was pausing its advertising assault against Mr. Heller, insisting it was doing so because of his willingness to come to the White House meeting with Mr. Trump.

America First was founded by a group of Mr. Trumps loyalists many of them with deep connections to Mr. Pence, including Nick Ayers, a Republican consultant who is regarded as the vice presidents top political adviser. The group compared Mr. Heller to Representative Nancy Pelosi, the House Democratic leader, and vowed a seven-figure advertising campaign against him.

Mr. Heller, the only Senate Republican who will face voters next year in a state carried by Hillary Clinton in 2016, is the top target for Democrats facing a Senate map with few opportunities in 2018. And there were already seven groups a mix of health care advocacy organizations and more partisan Democratic efforts on the air in Nevada assailing the Republican health care overhaul, according to a Republican ad buyer tracking the ad traffic.

Neither Mr. McConnells office nor his top outside political advisers were warned about an impending attack on one of their most endangered incumbents. They didnt check in with anybody, said Josh Holmes, Mr. McConnells former chief of staff. There was no clearing of channels, no heads-up, nothing.

Republican senators across the ideological spectrum have indicated their unease with the health bill. But Mr. Trump has few ties with the group, and several Republicans who remain on the fence have tangled with Mr. Trump, either during the presidential campaign or since.

Top Trump lieutenants like Stephen K. Bannon, his chief strategist, who lobbied members on the House bill, have been all but sidelined. Mr. Priebus has also played a much diminished role.

Mr. Pence has been far more active in seeking out Republican senators. Seema Verma, Mr. Pences former adviser in the Indiana Statehouse and now a top administration health care official, has also been trying to reassure senators that their states will have flexibility on Medicaid under the bill, while Mr. Pences former chief of staff, Marc Short, now the White House legislative affairs director, has been quarterbacking the effort from his hideaway in the Capitol.

Until Tuesdays meeting at the White House, Mr. Trump had spoken with only a few members of the Senate, according to an administration official. The pace was nothing like the dozens of calls he made to help pass the Houses health bill, aides said.

A senator who supports the bill left the meeting at the White House with a sense that the president did not have a grasp of some basic elements of the Senate plan and seemed especially confused when a moderate Republican complained that opponents of the bill would cast it as a massive tax break for the wealthy, according to an aide who received a detailed readout of the exchange.

Mr. Trump said he planned to tackle tax reform later, ignoring the repeals tax implications, the staff member added.

After the meeting, Mr. Trump played the role of cheerleader on Twitter, encouraging his weary Republican allies to keep working.

I just finished a great meeting with the Republican Senators concerning HealthCare, he wrote. They really want to get it right, unlike OCare!

A version of this article appears in print on June 28, 2017, on Page A1 of the New York edition with the headline: Trump Steps In With Late Pitch To Wary Senate.

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