Republican big guns took to the airwaves on Sunday, promising to shoot down healthcare reforms that have been passed by Congress and now upheld by the highest court in the land.

Following the supreme court's landmark decision this week – which ruled so-called Obamacare to be constitutional – the White House called for a line to be drawn on the issue.

But making the rounds on the Sunday morning political chatshows, the top two Republicans in Congress vowed to push ahead with efforts to repeal the 2010 law.

"This has to be ripped out by its roots," House of Representatives speaker John Boehner told CBS's Face the Nation.

He added: "We will not flinch from our resolve to make sure this law is repealed in its entirety."

The House, controlled by Republicans, has scheduled a vote on July 11 to repeal the law – a move that is likely to be blocked by the Democratic-led Senate.

The upper House's Republican minority leader Mitch McConnell told Fox News Sunday that his party will push the Senate to hold a ballot on the controversial healthcare reforms ahead of November's presidential run-off.

He added that if Republicans take the Senate in the national elections, "I commit to the American people that the repeal of 'Obamacare' will be job one."

In so doing, he echoed the pledge of Mitt Romney, who said he'd get the job done on his first day in office, if elected president.

Under the Patient Protection and Affordable Care Act, passed in 2010 following a protracted Washington battle – some 30 million Americans currently frozen out of the healthcare system will get coverage.

But under the controversial individual mandate, many citizens will be forced to pay for insurance, or face a penalty fine. Last week, the supreme court ruled that the provision was constitutional as a tax.

On Sunday, the White House reiterated its plea for opponents to the reforms to accept the justices' ruling, and move on from the issue.

"I think the thing that the American people want is for the divisive debate on healthcare to stop," White House chief of staff Jack Lew told Fox News Sunday.

"I think that what we need to do is get on with the implementation now, and that's what we intend to do," Lew added.