The two most powerful Republicans in Congress on Wednesday reiterated their determination to repeal Obamacare ― and said they look forward to finally passing a bill now that a fellow Republican, Donald Trump, is about to become president.

In a pair of celebratory but relatively muted press conferences, House Speaker Paul Ryan (R-Wis.) and Senate Majority Leader Mitch McConnell (R-Ky.) each cited repeal of the president’s signature health care law as a major priority for the next legislative session.

In the Senate press conference, a reporter asked McConnell directly whether he intended to move on the Affordable Care Act “right away.”

McConnell didn’t answer with a yes or a no, but he said: “It is a pretty high item on the agenda. I would be shocked if we did not move forward to keep our commitment to the American people.”

Ryan expressed similar sentiments at his press conference, saying that the “health care law is not popular.”

The statements are not at all surprising. House Republicans have passed bills to repeal the law more than 50 times, and in January, the Senate finally passed a version of a repeal bill as well.

Of course, Republican leaders have also promised to replace the law with an alternative health care scheme. So has Trump. But they have never agreed on the specifics of a replacement scheme ― instead endorsing policy outlines with modest levels of detail, at most.

Experts who have looked at these alternatives and inferred the details have determined that GOP plans would typically result in far fewer people with insurance, less financial protection for people with insurance, or some combination of the two ― reversing Obamacare’s historic progress toward expanding coverage, in part or in whole.

For example, one recent analysis, published by the Commonwealth Fund and written by scholars at the RAND Corporation, estimated that a fully fleshed-out version of Trump’s reform outline would result in between 16 million and 25 million people losing health insurance.

To be clear, a “repeal-and-replace” course of action, whatever form it took, would likely also benefit some people and groups.

Young people in good health would likely end up with access to cheaper coverage, since insurers would not be under the same restrictions to provide coverage to everybody at relatively uniform prices.

Taxes on the wealthy and on various parts of the health care sector, which the law uses to finance its expansion of health insurance, would come down.

But with Obamacare about to enter its fourth year of full operation, any substantial changes would cause major disruption, perhaps enough to give Republicans pause ― if not because of the human cost, then because of the potential for a political backlash.

Trump’s intentions are a wild card here. He attacked Obamacare regularly on the campaign trail and emphasized the possibility of repeal during the final weeks, following news of steep premium increases for the law’s regulated insurance policies in many parts of the country.

But Trump also vowed to replace the law with a program that would provide “great health care at a fraction of the health care cost.” It’s not clear how he’d react if Congress were to seriously take up an alternative, forcing him to confront the very real trade-offs that repeal-and-replace would entail.

Another unanswered question is how Republicans would handle repeal in the Senate, where they have a majority but not the 60 votes they would need to break a potential Democratic filibuster. In January, the Senate used a special legislative process called “reconciliation ,” which is reserved for certain budget-related items and can pass with a simple majority.

But the rules of reconciliation limit what a repeal-and-replace bill could include. When asked about the possibility of using reconciliation, McConnell would not say whether he intends to try it again, or whether he’d pursue repeal-and-replace through regular order — assuming Republicans don’t decide to change Senate rules altogether, so that filibusters are no longer possible.

Michael McAuliff contributed reporting.