The House Democratic leader, Representative Nancy Pelosi of California, did not pass up such a gift from the president. She wrote on Twitter that Trumpcare, as she called it, was “not only ‘mean,’ but a moral monstrosity.”

“The Senate bill is just as cruel,” she added, although no bill text has been released.

Republican senators were already planning to make their bill more generous, at least relative to the House bill, known as the American Health Care Act. At the Capitol, the Senate majority leader, Mitch McConnell of Kentucky, said Republicans were hard at work on their legislation, although he did not divulge any specifics about it.

“Our goal here is to move forward quickly,” he said. “The status quo is unsustainable.”

The Congressional Budget Office found that the bill passed by the House would leave 14 million more people uninsured next year than under the Affordable Care Act, and 23 million more in 2026. It also said that the House bill would cut more than $800 billion from projected federal spending on Medicaid over the next 10 years and that less healthy people could face “extremely high premiums,” as would some older Americans.

For example, the budget office said, for a typical 64-year-old with an annual income of $26,500, the net premium in 2026 — after tax credits — would average about $16,000 a year under the House bill, compared with $1,700 under the Affordable Care Act.

Doctors and hospitals opposed the House bill, as did groups like the American Cancer Society and AARP. Senate Republicans immediately dismissed the House overhaul and pledged to write their own replacement for the health law.

Senate Republicans have been working for weeks on proposals that they say could soften the effects of the House bill by providing more financial assistance to low-income people and older Americans to help them pay for insurance.

But some Republican senators are eager to keep a provision of the House bill that would let states opt out of a federal requirement for insurers to provide certain minimum health benefits.