But Friday came and went without any agreement or public show of progress — and with no vote in sight. Instead, Mr. McConnell was dealing with a new dose of uncertainty about whether Republicans should continue on their current course or scrap their bill for a repeal-only measure that would probably have at least as much difficulty garnering enough votes to pass.
The health care debate almost certainly will continue deep into July, when Congress will face other pressing issues, including raising the government’s statutory borrowing limit.
“We need repeal; we need replace,” Mr. Sasse said on Fox News. “Trying to do them together hasn’t seemed to work.”
Republican leaders in Congress had embraced the repeal-now-replace-later mantra after Mr. Trump’s election, envisioning legislation that would end the Affordable Care Act in a few years as they worked on a replacement. But that plan was blown up quickly in January when Mr. Trump publicly demanded that a replacement be adopted simultaneously. Since then, Mr. McConnell and Speaker Paul D. Ryan have choreographed a complicated legislative dance that would fulfill Mr. Trump’s repeal-and-replace wishes.
Now, those wishes could be changing.
In his letter to the president, Mr. Sasse said that if a deal on a revised health care bill had not been struck by the time the Senate returned from its recess on July 10, Mr. Trump should call on Congress to “immediately repeal as much of Obamacare as is possible” under the rules that must be followed to avoid a filibuster, with a one-year delay on the repeal bill’s implementation.
Then, he said, lawmakers should get to work on replacing the health law and should cancel their planned August recess.
“On the current path, it looks like Republicans will either fail to pass any meaningful bill at all, or will instead pass a bill that attempts to prop up much of the crumbling Obamacare structures,” Mr. Sasse wrote. “We can and must do better than either of these — both because the American people deserve better, and because we promised better.”
Soon after Mr. Sasse’s appearance on Fox News, Mr. Trump wrote on Twitter, “If Republican Senators are unable to pass what they are working on now, they should immediately REPEAL, and then REPLACE at a later date!”
Asked about the tweet, a White House spokeswoman, Sarah Huckabee Sanders, said, “The president hasn’t changed his thinking at all.”
“We’re still fully committed to pushing through with the Senate at this point,” she said. “But we’re looking at every possible option of repealing and replacing Obamacare.”
Mr. McConnell was hoping that the Senate would pass his bill this week. But he dropped that idea on Tuesday after it became clear that he did not have the votes and would have to revise his bill for it to have any chance of passing. A spokeswoman for Mr. McConnell declined to comment on the president’s tweet.
Mr. Trump has weighed in as Senate Republicans are struggling to decide how much of the Affordable Care Act should be eradicated and how much should be retained. In the Senate this week, Republicans veered from their original approach and said they were discussing whether to keep a tax imposed by the Affordable Care Act on the investment income of the most affluent Americans. The revenue could be used to increase insurance subsidies for lower-income people.
Subsidies in the Senate bill were already beginning to look like those in the Affordable Care Act, which are tied to a person’s income and local insurance costs. However, the Senate subsidies are less generous than those under the current law.
The repeal bills written by House and Senate Republicans would provide tens of billions of dollars in assistance to health insurance companies to help stabilize insurance markets and hold down premiums. Many of the same Republicans attacked such payments, when made by the Obama administration, as a bailout for the insurance industry.
But as senators tried to come to agreement, Mr. Trump effectively added a distraction. A clean repeal of the Affordable Care Act would face huge political obstacles in the Senate if it was not accompanied by legislation to provide health coverage in some other manner. Republican senators are already faced with pleas from constituents who want the health law to remain in place. If they approve a repeal-only measure, they will face enormous pressure to explain what comes next.
Mr. Trump’s remarks on Twitter offered a reminder to congressional Republicans of how inconsistent the president has been as a partner. In May, he cheered passage of a House plan to repeal and replace the Affordable Care Act, only to later denounce the House bill as “mean.”
Senator Patty Murray of Washington, the top Democrat on the Senate health committee, said that with his tweet, Mr. Trump was “sending a signal to Senate Republicans that they can count on him to support their back-room deals to jam their bill through just about as much as House Republicans could count on him before he called their bill ‘mean.’”
Mr. McConnell is also facing pressure from restive conservatives inside and outside the Senate who are dissatisfied with his repeal bill. But placating them risks driving away other members of his caucus.
“It’s distressing to see so many Republicans who’ve lied about their commitment to repeal,” said Ken Cuccinelli, a former Republican attorney general of Virginia who is now the president of the Senate Conservatives Fund, which supports conservative candidates.
Conservatives are pressing Mr. McConnell to accept a proposal by Senator Ted Cruz, Republican of Texas, that would allow insurers to sell cheaper, less comprehensive health plans if they also offered at least one plan that met federal insurance standards, including a requirement to provide certain benefits like maternity care and mental health coverage.
Mr. Cruz has said the proposal would increase the number of health insurance options available to consumers, allowing them to choose plans that would cost less because they did not have to comply with federal mandates.
But critics said the proposal was unworkable because less healthy people would gravitate to insurance plans that provide a full set of benefits, and they could face higher premiums, while healthy people would tend to choose lower-cost plans.
Mr. McConnell has said that the health law should be repealed “root and branch.” Andy Roth, a vice president of the Club for Growth, a conservative organization, complained on Friday that moderate Republicans in the Senate wanted to keep much of the health law in place.
“‘Root and branch,’” Mr. Roth said, “doesn’t mean trimming the hedges.”