House Speaker John A. Boehner (R-Ohio) leaves a news conference concerning upcoming budget negotiations. If a budget is not agreed upon, the government will shut down at midnight on Sept. 30. (Melina Mara/The Washington Post)

Congressional Democrats rejected GOP efforts Thursday to delay or curtail funding for President Obama’s health-care initiative, saying the strategy to block implementation of the law would lead to a government shutdown or a default.

Republicans have rallied to the idea of delaying the implementation of the Affordable Care Act as their main point of leverage. Some conservative groups have been pushing the idea of using government-funding legislation as a vehicle to strip away money for implementing the health-care law. But GOP leaders have tried to talk rank-and-file members out of that approach and instead have been pushing the idea of delaying some major pieces of the legislation.

That approach ran into fierce Democratic opposition Thursday when Senate Majority Leader Harry M. Reid (Nev.) told House Speaker John A. Boehner (R-Ohio) that Democrats had no intention of slowing the implementation of Obama’s landmark domestic policy achievement.

“I told him very directly that all these things they’re trying to do on the Obamacare is just a waste of their time,” Reid told reporters after the meeting.

The go-slow GOP strategy is designed to prevent a government shutdown, which would begin Oct. 1 unless Congress approves a new funding vehicle, and to avoid a showdown on the bid to increase the federal debt limit by mid-October. After several months of using extraordinary measures to keep the government afloat, the Treasury will run short of cash as soon as Oct. 18, according to independent estimates.

GOP leaders have been on the defensive for weeks after outside conservative groups began a campaign to try to force a showdown by attaching language to defund the health-care law to legislation that would provide money to keep federal agencies open. With Obama and Democrats opposed, senior Republicans say that such a strategy would lead to a government shutdown for which Republicans would pay a political price.

But many Republicans objected to Boehner’s initial plan to push through legislation that would extend current government funding levels to mid-December and attach a rider that would strip money for the health-care law — but one that the Senate would easily remove so it could send a clean funding extension to president.

GOP leaders delayed a vote on their plan until next week and the most conservative House Republicans began debating proposals they hope could attract Democratic support.

“The key is we’re going to do everything we can to protect the people of our districts from the harmful effects of this law,” said Rep. James Lankford (R-Okla.), a junior member of the leadership team.

One compromise idea would be to reverse some of the cuts that were mandated by the 2011 “sequester” deal. Democrats opposed those reductions, and the idea would be to restore that funding in exchange for a one-year delay for the health-care law.

Some conservatives are open to that approach. “Much stronger than what the leadership had recommended to us on Tuesday,” said Rep. Phil Gingrey (Ga.), who is running for the Senate. “I think it would be much more acceptable to my constituents in Georgia. They might not be totally satisfied with it, but much more so than what was proffered on Tuesday.”

That position was not sufficient for former senator Jim DeMint (R-S.C.), who runs the Heritage Foundation. He has led the push to force a government shutdown if necessary to compel Democrats to agree to strip funding for the health-care law, and he said Thursday that the fight should be focused on the Oct. 1 deadline.

“This is a must-pass bill.Our point is Republicans should fund the government in its entirety except for Obamacare,” DeMint said. “They should send that bill to the president, to the Senate, make it clear to Americans they don’t want government shutdown.”

Boehner declined to endorse any proposal Thursday. “There are a lot of members with a lot of ideas. And we’re going to continue to talk to all of them,” he told reporters.

The speaker met with Treasury Secretary Jack Lew on Wednesday and delivered a message that focused on the debt-ceiling showdown. Obama has said that he will not negotiate over the government’s borrowing authority, because it used to involve perfunctory action by Congress to pay the nation’s bill and should not be a political bargaining chip.

Boehner rejected the president’s claim and cited forLew examples of when Congress has wrangled concessions from presidents in exchange for extending borrowing limits.

Even if Obama is willing to haggle in exchange for a debt-limit increase, Democrats said Republicans need to find a different negotiating tool. “Look, the Republicans have a fetish about trying to kill Obamacare. When they go home to their districts, that’s what they hear,” said Rep. Chris Van Hollen (Md.).

Democrats also point to polling that shows that although the health-care law is not popular, the public does not want it repealed and does not want the government to shut down over the dispute.

“We have the high ground,” said Sen. Charles E. Schumer (N.Y.). “If we say to them, ‘We dare you, shut down the government unless you repeal Obamacare, we dare you, risk the full faith and credit of the United States until we end Obamacare,’ they will lose.”

Jackie Kucinich contributed to this report.