In the first hours after Republicans reclaimed the House, the presumptive new speaker, John Boehner (R‑Ohio), made clear his plans for the health care bill passed last March: “We must do everything we can to try to repeal this bill and replace it with common sense reforms to bring down the cost of health care.”

Voters made themselves abundantly clear on Tuesday — Democrats who supported the health care bill lost in droves. Eight Democrats in the House, including New York’s Scott Murphy, switched from opposing the bill on early votes to supporting it for final passage. Six sought re-election; five, including Murphy, lost. Arizona and Oklahoma passed ballot measures opposing the law’s individual mandate, and Colorado voters fell just short of doing likewise. Missouri voters had already done so earlier this year.

Election night exit polls showed that at least half of voters wanted to repeal the bill. While that is an almost unprecedented level of opposition for a major entitlement expansion, it may actually understate the anti-ObamaCare sentiment because exit polls tend to tilt Democratic. A better measure might be an election night Rasmussen telephone poll that found 59% of voters in favor of repeal. Another post-election survey found that 45% saw their vote as a specific message of opposition to the health care bill.

So as Republicans celebrate and Democrats pick through the electoral rubble, what can we expect to happen next with health care?

The new Republican House majority will undoubtedly schedule a quick vote on repealing the health care law, perhaps as early as January. It will pass the House quite easily; not only will every Republican vote for repeal, but there are still a dozen Democrats in the House who voted no last March.

But that is as far as repeal is likely to go. The Democrats remain in control of the Senate, and Harry Reid, returning in triumph, is unlikely to even schedule a vote.

Repealing ObamaCare is just not going to happen while Obama is in office.

Some Republicans may be willing to take their symbolic victory in the House and call it a day. They shouldn’t. There are many things they can do short of repeal that can begin the step-by-step dismantling of ObamaCare.

At the low end of the scale, Republicans should use their new investigatory powers to hold hearings and force officials like HHS Secretary Kathleen Sebelius to testify about the law. For example, since the law passed we have learned that health care spending will go up, not down as promised, and that millions of Americans will not be able to keep the insurance they have today. What does Sebelius think of that?

In addition, President Obama’s recess appointment of British-style rationing fan Donald Berwick as head of the Medicare and Medicaid systems expires with the new Congress. If Obama reappoints him, Republicans should use his hearings to explore how ObamaCare threatens the quality of American health care and access to it.

Next, Republicans should seek repeal of those parts of the new law that are unpopular with Democrats as well as Republicans. There are a lot of Democratic senators up for re-election in 2012 who represent states Republicans swept this year. They may not be willing to go all the way to repealing the law, but they may still be anxious to show that they got the voters’ message and are willing to work with Republicans to “fix it.”

For example, Democratic senators like North Dakota’s Kent Conrad have expressed concerns that the law’s new long-term care entitlement is “a fiscal time bomb.” Several Democrats have indicated a willingness to repeal the law’s requirement that even small businesses file a 1099 tax form for every vendor that they do $600 worth of business with. Even President Obama has indicated a willingness to revisit this provision.

ObamaCare would all but wipe out the popular Medicare Advantage program. With seniors having voted heavily against Democrats on Tuesday, there may be bipartisan support for revisiting cuts to that program. Congress could also look to repeal restrictions on popular options like Flexible Spending Accounts and Health Savings Accounts.

And the administration has already been forced to give some businesses temporary waivers from the law’s new insurance mandates. Congress could make those waivers permanent and offer them to other companies.

Speaking of waivers, Democratic Senator Ron Wyden of Oregon had asked for his state to be exempted from many of the law’s provisions, including the individual mandate. Republicans should push to give it to him, and encourage other states to apply as well.

Republicans should also start laying out their own positive alternatives. It’s not enough to simply repeal ObamaCare. Republicans will have to show that they have their own proposals for dealing with health care costs and the uninsured. They had a number of good ideas during the debate over reform, ranging from allowing the purchase of insurance across state lines to changing the tax treatment of individually owned insurance, but those ideas couldn’t get much of a hearing while the president controlled the agenda. Now they can.

Finally, Republicans in the House now control the power of the purse. They should refuse to fund implementation of the bill. For example, the IRS says it will need to hire as many as 13,500 additional IRS agents to administer the law’s unpopular individual mandate. Congress should refuse to appropriate the money to do so. All sorts of provisions could be subject to defunding. Theoretically, the House could go so far as to forbid HHS officials from spending any time working on any aspect of the law.

Cutting off funding risks having the Democrats shut down the government in an attempt to put public pressure on the Republicans to pass a budget with the health care funding that the president wants. President Clinton used this tactic successfully against the Republican Congress in 1996. But the public, as shown by this election, is in a very different mood now. And Obama is no Bill Clinton.

Of course, the real battle over ObamaCare will be fought two years from now in the 2012 presidential elections. But there is still a lot to be done between now and then.