Eager to show who’s now in charge, the House’s new Republican majority plans to vote to repeal President Barack Obama’s landmark health care overhaul before he even shows up in their chamber to give his State of the Union address.

Though full repeal is a longshot — the House vote would be just the first, easiest step — they’ll follow up with dozens of attempts to hack away at what they derisively call “Obamacare.”

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The strategy is not risk-free for the Republicans, who won’t have a replacement plan of their own ready by the time of the repeal vote. But they say there’s no time to lose.

Senate Democratic leaders are sending their own “you-don’t-scare-me” message. In a letter Monday to House Speaker-to-be John Boehner, they served notice that they’ll block any repeal, arguing it would kill popular provisions such as improved prescription coverage for Medicare.

All the while, the Obama administration intends to keep putting into place the law’s framework for covering more than 30 million uninsured people. Ultimately, Obama still has his veto pen, and Republicans aren’t anywhere close to the two-thirds majorities they would need to override.

Most likely, both parties will carry the main issues of the health care debate into the 2012 presidential election, when Obama is expected to seek a second term and House and Senate control will be up for grabs again.

It’s not going to be easy; it’s going to be a long, hard slog,” said Rep. Steve King, R-Iowa, an early leader in the repeal drive. The quick thumbs-down vote by the House will have “tremendous utility and value,” King said, but it may take electing a Republican president in Obama’s place to accomplish the overall goal.