Sam Kazman of the Competitive Enterprise Institute and Ron Pollack of Families USA weigh in on the Supreme Court's ruling upholding subsidies available under the Affordable Care Act. (AP)

Rep. Dave Brat stood just off the House floor Thursday, minutes after the Supreme Court had rejected the latest challenge to the Affordable Care Act, and gathered his thoughts.

“Just a shocker,” the Virginia Republican said, echoing the reaction of many fellow conservative lawmakers. “How the brightest legal minds could come to that conclusion is beyond me.”

But, after the initial reaction, the big question that raced through political and policy circles, especially Republican ones, was: What happens now?

At least in Congress and the courts, probably not much. Despite expressing renewed resolve to repeal the health law, congressional Republicans know any such effort would face a certain veto from President Obama. And they are far from united on any particular plan.

Meanwhile, legal challenges to the law remain, but none poses as serious a threat as King v. ­Burwell, which aimed at a pillar of the law — the insurance subsidies being provided to millions of people through the federal exchange.

Most of the near-term action on the law, in fact, will occur in insurance companies, hospitals and government offices where people are working furiously to implement a complicated statute in a fast-changing environment.

“All the challenges that existed yesterday are still there,” said Larry Levitt, a senior vice president at the Kaiser Family Foundation. One of the biggest is making sure enough people enroll in the exchanges to make them work right.

On Capitol Hill, Rep. Tim Huelskamp (R-Kan.) said Thursday he hoped Republican leaders would seek to use special budget rules, known as reconciliation, to overcome Democratic opposition and send a bill repealing the health law to Obama. “We have never put anything on his desk,” he said.

But House Speaker John A. Boehner (R-Ohio), ducked questions about using reconciliation and declined to say whether Republicans would draft a health-law alternative. His committee chairmen had been figuring out what to do if the justices ruled their way, he said, and now needed to refocus their efforts.

Sen. John Barrasso (R-Wyo.), an orthopedist who has served as the health-care point man for Senate Republicans, named one of the proposals to replace the law — but when pressed on whether Republicans would consider repeal legislation, replied: “We know we do not have a willing partner in the White House. We know that the president would veto anything that would pass, and as a result we need someone new in the White House who’s a willing partner to actually help get people the care they need from a doctor they choose at lower cost.”

Upholding affordable health care

Rep. Tom Cole (R-Okla.), a senior GOP member who is close to Boehner, said using budget reconciliation to repeal the entire law would not be the best tool to use. “We ought to put something on the president’s desk that we have a chance that he might sign,” he said.

Other Republicans mentioned targeting unpopular revenue provisions, including taxes on medical devices and on the most generous health plans.

Democrats, meanwhile, bluntly told Republicans to move on. “I think they should get real and forget about Obamacare,” said Senate Minority Leader Harry M. Reid (D-Nev.).

Meanwhile, the people who are trying to make the law a success are focusing on myriad challenges, including trying to make sure that enrollment — which has been slower than initial projections — picks up. If enrollment levels off, “That would be troubling and exchanges need to focus on how to better do outreach and continue to get people to sign up,” said Caroline Pearson, a senior vice president at Avalere Health, a consulting firm.

At the end of March, federal health officials said 10.2 million people had signed up in state and federal exchanges and had paid their first month of premiums. But if the attrition rate from 2014 is repeated in 2015, Avalere estimates that total enrollment would fall to 9.2 million by the end of this year. At that pace, it would be difficult to hit the Congressional Budget Office projections of 25 million people enrolled by 2017.

While exchanges have succeeded in enrolling very low-income individuals, they’re having trouble attracting middle and higher-income individuals, according to an Avalere analysis.

“That’s not politically sustainable, and it’s not financially sustainable if you are only enrolling the low-income people,” said Robert Laszewski, a health insurance industry analyst.

Without a robust enrollment with the right mix of individuals to share the risk, insurers are more likely to have higher costs and push for big premium increases; some are seeking double-digit increases for some plans for next year.

Analysts said that Thursday’s Supreme Court ruling also makes it more likely that some state exchanges with financial problems will convert to the federal exchange, now that subsidies aren’t in danger. In addition to Hawaii and Vermont, where officials have talked about making such a move, the exchanges in Colorado and Minnesota face serious financial troubles and would be among those to consider such a move, analysts said.

A little-noticed provision in the law could be another focus for conservative opponents to challenge the law, beginning in 2017.

The provision, known as Section 1332, could allow a Republican president to waive some of the main components of the law in conservative states that want to take a different approach to health policy, experts say. These waivers could allow governors to put their own imprint on health reform and potentially eliminate some of the more controversial parts of the ACA, including the requirement that most Americans have insurance.

The Supreme Court ruling, while solving an immediate political problem for Republicans, creates one further down the road.

“It puts a lot of pressure on Republicans to have credible options other than to repeal Obamacare,” said Joseph Antos, with the American Enterprise Institute. “You have to be more specific than repeal. The average voter wants something constructive coming out of this, not something destructive.”

On the legal front, health policy experts say the King v. Burwell decision dispenses with the last major hurdle to the ACA, with only a few challenges, including some involving contraceptive coverage, still on the radar.

Arguably the most important is House Speaker Boehner’s lawsuit against Obama. The suit focuses on the administration’s actions to delay the law’s employer mandate and to reimburse insurance companies to reduce health-care costs for lower-income people. Republicans argue the money was never specifically appropriated; the White House says it is spending the money properly.

The case is pending in the U.S. District Court for the District of Columbia.

Michael Cannon, a health policy expert at the Cato Institute and an architect of the King challenge, said the House suit could be “dangerous” to the ACA but said he doubts the House would be granted standing to sue because it would have to establish that it had been injured by the administration’s actions.

Critics of the House suit agreed. “I think Speaker Boehner’s challenge will come to nothing,” said Walter Dellinger III, a former acting solicitor general, in a conference call with reporters. “The Supreme Court is not a place to air political grievances.”

Robert Gebelhoff, Paul Kane and Ed O’Keefe contributed to this report.