Shutting down the government for two weeks did nothing to stop Obamacare, but Sen. Ted Cruz, R-Texas, is promising more bruising battles against the health care law.

In an interview with the Wall Street Journal published Thursday, Cruz said that he considers "elevating the debate on Obamacare" to be his top accomplishment of 2013. The conservative senator last year helped bring on the shutdown in October after insisting for several weeks on defunding the Affordable Care Act before letting a government spending bill pass.

Cruz said he intends to "fight even harder” now to “repeal every word of Obamacare,” adding that the next opportunity to roll back the law comes with the spending bill Congress must pass by Jan. 15 in order to avert another shutdown.

In the 45-minute interview, Cruz mentioned Obamacare more than 40 times, the Journal noted, saying that Republicans must use “every leverage point available” against it.

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Not all conservative lawmakers are on board with Cruz’s aggressive approach. “That was a failed strategy," Sen. Ron Johnson, R-Wis., said, the Journal reported. "This year, let's not have shutdown fights."

However, the GOP is not exactly shifting its focus from the health law. The Republican-led House of Representatives is slated this week to consider two bills related to the Affordable Care Act. The “Exchange Information Disclosure Act” and the “Health Exchange Security and Transparency Act” will both go the House floor on Friday in an attempt to bring more transparency to the workings of the Obamacare marketplaces.

House Speaker John Boehner, R-Ohio, said Thursday the bills are part of an ongoing effort “to protect the American people from the consequences of this disastrous law.”

Still, he said, “Our primary focus will continue to be jobs and the economy,” citing legislation passed by the House and ignored in the Senate.

House Minority Leader Nancy Pelosi, D-Calif., on Thursday slammed for Republicans for their opposition to the Affordable Care Act. She noted that more than 2 million people have so far enrolled for private insurance via Obamacare, around 4 million have signed up for Medicaid, and around 3 million young adults are on their parents’ insurance plans because of the law.

“They’re saying let’s do everything we can to take away health insurance from 9 million who already have it and prevent many more from getting it,” she said.