The activists at Heritage Action, one of the conservative groups that successfully persuaded enough Republicans to refuse to fund the government unless the federal health care law is defunded, is not sorry about the shutdown.

And Michael Needham, CEO of Heritage Action, thinks that if this goes on long enough, Democrats will have no choice but to back down.

More than a week into the first government shutdown since the Bill Clinton era, groups such as Heritage Action on the right continue to urge lawmakers not to negotiate a measure to fully fund the government unless they include riders to effectively dismantle the Affordable Care Act, also known as Obamacare.

“The only acceptable way out of this is some sort of deal that funds the federal government without funding Obamacare,” Needham told reporters at a breakfast on Wednesday sponsored by the Christian Science Monitor. “This is a fight about Obamacare, and the attention of Republicans and conservatives needs to be back on Obamacare and not on other ways out of this situation.”

The group’s doggedness about the GOP strategy, combined with muscle on the inside from dozens of conservative House members and Republican Sens. Ted Cruz of Texas and Mike Lee of Utah, puts Republicans in a tough position going into negotiations to resolve the impasse with Democrats. The group’s regularly updated legislative scorecard, which tracks votes and issues it believes help separate the conservatives from the RINOS (Republicans In Name Only), serves as a public shaming mechanism for Republicans that wander astray.

In August, the group ramped up the pressure by joining with its sister organization, the Heritage Foundation, for a nine-city town-hall tour that drummed up support in the states for the plan to link Obamacare defunding to must-pass legislation like the bill to fund the government.

By some measures, the campaign has worked. Before the government shut down earlier this month, Republican House Speaker John Boehner and party leadership planned to adopt a different strategy that would have used the vote to increase the debt ceiling — not the government funding bill — to wage its war on Obamacare. In the final days before the funding deadline, Boehner backed down to voices within his House conference to adopt the Heritage-Cruz strategy, which resulted, unsurprisingly, in the government shutdown.

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Since then, House Republicans have passed several minifunding bills that would re-open some crucial and popular parts of the government, which the Democrat-led Senate and President Barack Obama have repeatedly rejected. Needham said he supports the strategy.

“If we want to sit on a government shutdown over the next several weeks over the [National Labor Relations Board] and the [Environment Protection Agency] being shut down, I’m perfectly happy to sit in that situation until Obama stops this unaffordable and unfair law,” Needham said.

It is assumed, however, that Obama never will agree to defund the health care law — the signature legislative achievement of his presidency — which makes the future of this current battle uncertain.

Some Republicans appear to have conceded, too, that they can’t fully defund the law, which is why they have proposed less stringent conditions to re-opening the government, such as delaying the individual mandate to buy health insurance and an unpopular tax on medical devices.

As the Oct. 17 deadline to increase the federal debt limit draws near, it remains uncertain whether Republicans will even remain steadfast in their demand to cripple part of the health care law. In recent days, House Republican leaders have spoken more about their demand for any kind of formal negotiation with Democrats than a call to defund or delay the law. On Wednesday, Republican House Budget Committee Chairman Paul Ryan published an op-ed in the Wall Street Journal that outlined possible paths forward, and none mentioned Obamacare.

That omission certainly caught Heritage Action’s attention.

“This is a fight about Obamacare,” Needham said when asked about Ryan’s op-ed. “And the attention of Republicans and conservatives needs to be back on Obamacare and not on other ways out of this situation.”