The Republican health-care plan moving rapidly toward a crucial House vote this week is likely to be changed to give older Americans more assistance to buy insurance, Speaker Paul D. Ryan said Sunday.

"We think that we should be offering even more assistance than what the bill currently does," Ryan, R-Wis., said in a "Fox News Sunday" interview, in which he confirmed that House leaders are eyeing a Thursday vote on its passage.

Meanwhile, a key conservative senator said White House officials were continuing to negotiate through the weekend on even more dramatic revisions to the bill in hopes of winning over hard-liners who have threatened to tank the legislation.

Sen. Ted Cruz, R-Texas, said he and two other conservative leaders - Sen. Mike Lee, R-Utah, and Rep. Mark Meadows, R-N.C., chairman of the House Freedom Caucus - met at President Donald Trump's Mar-a-Lago resort in Florida in an attempt "to fix this bill."

"I cannot vote for any bill that keeps premiums rising," Cruz said, echoing the concerns of other hard-line lawmakers who want the legislation to undo more of the Affordable Care Act's insurance mandates. "President Trump said this is one big, fat negotiation. Here is the central prize: If we lower premiums, and hopefully lower them a lot, that is a victory for the American people."

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"It's a fine needle that needs to be threaded, no doubt about it," said Health and Human Services Secretary Tom Price, speaking about the negotiations Sunday on ABC's "This Week."

Ryan's declaration that more would be done to help older Americans came after a third House moderate said Saturday that he could not support the bill "in its current form."

Rep. Brian Fitzpatrick, R-Pa., who represents a suburban Philadelphia district that has been heavily targeted by Democrats, said in a Facebook post that he was most concerned that the legislation would roll back efforts to prevent and treat opioid abuse.

But he said that was one concern of many, and lawmakers from across the GOP's ideological spectrum have expressed fears that the American Health Care Act will not drive down prices. Reps. Ileana Ros-Lehtinen, R-Fla., and Leonard Lance, R-N.J., have cited that concern in announcing their opposition to the bill, and several other moderates remain undecided.

Those fears were stoked last week by a Congressional Budget Office analysis that forecasted a short-term increase in premiums under the GOP law, and while premiums are expected to drop by roughly 10 percent over a 10-year horizon, some older and low-income people would face massive premium hikes.

Those over 50 but not yet 65 - and thus eligible for Medicare, the federal health program for seniors - represent a major issue in forging an alternative to the ACA. That age group tends to have more medical issues than younger adults and, thus, higher insurance costs, and the ACA forbids insurers to charge their oldest customers more than three times their rates for young adults - essentially having young adults cross-subsidize the cost of coverage for older ones.

But House Republicans want to eliminate that feature of the law, and the GOP bill would allow a five-to-one ratio as part of an attempt to attract more of the younger, healthier customers whom insurers want.

In an extreme case laid out in the CBO report, a 64-year-old earning $26,500 a year would see yearly premiums rise from $1,700 under the ACA to $14,600 under the Republican plan.

Ryan questioned that analysis, suggesting that administrative actions taken by the Trump administration would further lower premiums and questioning whether the ACA would remain viable in a decade. But he acknowledged that the GOP bill would probably have to change.

"We believe we should have even more assistance, and that's one of the things we're looking at for that person in the 50s and 60s because they experience higher health-care costs," he said.

The GOP bill as currently written offers a fixed tax credit for low- and middle-income Americans that rises by age. But it does not rise and fall, like the ACA's subsidies, so a person pays only a fixed percentage of their income on their health insurance premiums. That, according to the CBO estimate, leads to substantial cost savings that - together with cuts to Medicaid - allow the GOP plan to eliminate nearly all of the taxes imposed under the ACA.

Trump won the support of several conservative House members on Friday when he agreed to make changes to the Medicaid portion of the bill, including giving states the option of instituting a work requirement on childless, able-bodied adults who receive the benefit.

But Sen. Rand Paul, R-Ky., who has worked closely with the hard-right bloc in the House, said on "This Week" that the bill was still short of a majority.

"They still believe that the conservatives in their caucus don't want Obamacare Lite," he said. "I believe that the real negotiation begins when we stop them. You have to stop them."

Paul noted that he passed out notes based on Trump's book "The Art of the Deal" at a meeting he had with Freedom Caucus members last week: "We need to learn from the master, and let's make sure that we increase our leverage by holding the line."

But Ryan expressed confidence that the bill would pass the House this week - and then move to the Senate, where the legislation is facing even sharper doubts and the GOP majority is much narrower. He cited Trump's hands-on involvement as a key factor is moving the legislation forward.

"We are making fine-tuning improvements to the bill to reflect people's concerns, to reflect people's improvements," he said. "The president is bringing people to his table, and I'm very impressed with how the president is helping us close this bill, and making the improvements that we've been making, getting the votes. ... We are right where we want to be."