For outside groups and conservative politicians aiming to make names for themselves, there's still plenty of incentive to attempt the impossible.

Sure the Republican-controlled House might have voted to repeal all or part of Obamacare more than 30 times over the last two years, the conservative-leaning Supreme Court might have upheld its core constitutionality and voters may have returned the man whose name is branded on it to the presidency, but that doesn't mean conservatives are done pressing for its removal.

"We have an enduring belief that consent of the governed is a necessary component of any legislation and especially such sweeping legislation. This law doesn't have it. Still doesn't have it," says Ken Hoagland, chairman of Restore America's Voice, a conservative political action committee. He adds that his group, who launched grassroots efforts to press for repeal since its 2010 passage, is applauding Texas Sen. Ted Cruz's bill, filed Tuesday, to repeal the sweeping heath care reform legislation and plans to launch a television advertising campaign in support of repeal.

"We will start running national TV ads and collect more petitions in support of it," Hoagland says, though he declined to say how much money his group would spend on advertising. He describes the buy as a national effort focused on cable news channels such as MSNBC and Fox News.

Hoagland says many Americans oppose Obamacare and despite the clear unlikelihood that the Democratically-controlled Senate would even take a vote on Cruz's bill or that President Barack Obama would sign a measure rolling back one of his signature legislative accomplishments, it's worth the effort to try.

"There's still an enduring cynicism about Obamacare, whether it will help us or hurt us," he says. "No one is disputing that the author's advanced it as a way to help the country. What's really happening here is that a lot of Americans still believe that their hopes were ill-founded, that this will hurt the United States."

Hoagland says his group will make similar efforts on tax reform and balancing the federal budget in the coming months. The PAC raised $4.6 million during the 2012 election cycle and spent $4.5 million, according to the Center for Responsive Politics.

And despite the dim prospect of legislative success, Cruz, a Tea Party-backed candidate who knocked off a better known and established Republican during his primary, reaps political rewards simply for proposing the repeal.

At a time when other Republicans seem to be tempering their conservatism in exchange for political compromise – think the House GOP who recently backed down from a political fight on the debt ceiling and Sens. John McCain and Marco Rubio who are pursuing bipartisan immigration reform – Cruz is going all-in, Texas Hold 'Em style.

"Politics requires compromise and I'm quite sure that Senator Cruz understands that, but there are some things you have to stand your ground on," says Hoagland, who worked with Cruz on school choice reform in Texas in the past. "Look, right at the center of that statement, the country is built on the premise of the consent of the governed."

"I think this man has a pretty much unlimited future in American politics. He could go all the way," he adds.

Cruz's repeal bill has 32 co-sponsors, all Republicans, according to a press release, which acknowledges its own quixotic nature.

"Unfortunately, this bill will not pass in the current Congress, but I will continue working hard until we have the votes to repeal Obamacare in its entirety," Cruz said in the release. "I will continue to work for Texans to expand coverage through effective free-market reforms and to protect the integrity of the doctor-patient relationship."

The White House has said it continues to support the legislation and is moving forward with implementation, scheduled to take full effect in 2014, after the Supreme Court upheld its individual mandate last summer.

Among other things, the measure provides increased funding for low-income Americans to obtain insurance, will eventually require all citizens to purchase insurance and mandates health insurance companies to maintain certain levels of coverage. The Obama administration has argued it will hold down health care costs, and although growth has slowed on that front, insurance premiums for many have still increased in recent months.