House Budget Committee Chairman Paul Ryan (R-Wis.), left, and House Majority Leader Eric Cantor (R-Va.) published op-eds in the Wall Street Journal and The Washington Post on Wednesday calling for President Obama to come to the negotiating table — but neither mentioned the Affordable Care Act as an item to be discussed. (JONATHAN ERNST/REUTERS)

Key GOP figures on Wednesday sent their clearest signals that they are abandoning their bid to immediately stop the federal health-care law — the issue that forced the government to shut down — and are scrambling for a fallback strategy.

Republican Party leaders, activists and donors now widely acknowledge that the effort to kill President Obama’s signature initiative by hitting the brakes on the government has been a failure. The law has largely disappeared from their calculus as they look for a way out of the impasse over the shutdown and for a way to avoid a possible default on U.S. debt.

Instead, they are regrouping for a longer battle over the health-care law. They also are trying to refocus the upcoming debt-ceiling showdown on fiscal issues, including entitlements and tax reform.

The strategy to defund the Affordable Care Act “needed a Plan B, and its authors, if they had one, didn’t share what it was,” said Heather R. Higgins, head of the Independent Women’s Forum and founder of a coalition of conservative groups seeking repeal of the health-care law.

The push to defund the legislation has cost Republicans politically. A Gallup poll released Wednesday found that only 28 percent of Americans view the Republican Party favorably — down 10 percentage points since September, and the lowest number for either party since Gallup began asking the question in 1992.

How the shutdown affects departments

Democrats took a smaller hit in the survey, with 43 percent of respondents viewing Obama’s party favorably, down four percentage points from last month.

Some Republicans are aiming harsh recriminations toward those who had vigorously advocated linking the funding needed to keep the government operating to the drive to stop the health-care law. Freshman Sen. Ted Cruz (Tex.), who has become the face of that strategy, is the chief target of such criticism from within GOP ranks.

“I think it was very possible for us to delay the implementation of Obamacare for a year until Cruz came along and crashed and burned,” anti-tax activist Grover Norquist said.

But Cruz spokeswoman Catherine Frazier said: “The American people remain behind the defund effort. Americans deserve negotiations. They don’t want Obamacare. Public opinion is behind this, and that should be enough for Democrats to come to the table and provide relief for all Americans.”

House Republican leaders — who had been backed into the shutdown strategy by demands from Cruz and tea party forces — have been trying to recalibrate since the shutdown began Oct. 1.

The latest signs of the shift came in editorial columns Wednesday by House Majority Leader Eric Cantor (R-Va.) in The Washington Post and Budget Committee Chairman Paul Ryan (R-Wis.) in the Wall Street Journal.

Both implored Obama to negotiate the debt ceiling — but, tellingly, neither mentioned the health-care law as an item to be discussed. Instead, they focused on entitlements, and Ryan wrote that there are many potential areas of agreement between Obama and the Republicans.

The president has expressed a willingness to negotiate on long-term fiscal problems, but only if Republicans first vote to reopen the government and remove the threat of a federal default.

On Tuesday, House Speaker John A. Boehner (R-Ohio) also made no mention of the health-care law when he delivered a statement on the shutdown and the Oct. 17 deadline to raise the debt ceiling.

Boehner spokesman Brendan Buck insisted that Republicans have not given up on their demand that concessions on the health-care legislation be part of any deal to reopen the government. He acknowledged, however, that the demand has shifted from defunding the law — the original rallying cry — to a much narrower goal of delaying a requirement that uninsured individuals obtain coverage.

Some of the most influential players in the conservative movement also were taking pains Wednesday to maintain their distance from the shutdown strategy, while reaffirming their opposition to Obamacare.

The chief lobbyist for Koch Industries sent a letter to Capitol Hill offices saying the company’s owners — heavyweight conservative donors Charles and David Koch — have never publicly supported the defund strategy, despite assertions by Senate Majority Leader Harry M. Reid (Nev.) and other Democrats to the contrary.

“Koch believes that Obamacare will increase deficits, lead to an overall lowering of the standard of health care in America, and raise taxes,” Koch lobbyist Philip Ellender wrote. “However, Koch has not taken a position on the legislative tactic of tying the [spending bill needed to keep the government open] to defunding Obamacare nor have we lobbied on legislative provisions defunding Obamacare.”

One major Koch-funded organization, Americans for Prosperity, has emphasized potential problems with the law but has kept its distance from efforts to defund it and from the shutdown strategy.

“We see this as a long-term effort,” said Tim Phillips, executive director of the group, which plans to resume a $6 million ad campaign against the law. “We think this effort continues into the fall of 2014 and even beyond.”

The Affordable Care Act’s online insurance exchanges have gotten off to a rocky start this month, and polls show the law remains unpopular.

Many GOP pollsters and strategists sharply criticized the push to defund the legislation as it gathered steam this summer, preferring a less confrontational approach that would build on public doubts about the law and focus on delaying its implementation.

The idea was that flaws in the legislation would become more apparent over time and that the continuing debate would motivate conservatives to vote in the 2014 midterm elections.

Now that plan is in tatters, and party and movement leaders are trying to salvage something from what is widely acknowledged to be a politically disastrous few weeks. Instead, many strategists say, the stumbling rollout of the law has been overshadowed by the shutdown and a perception that Republicans have overreached.

“There is a strong sense of a missed opportunity,” Norquist said.