With Congress in recess during August, the political world is focused on Oct. 1 — the date that President Obama’s health care law starts signing up participants and that the government will shut down without a budget agreement.

Sen. Mike Lee took to USA Today on Sunday to make the case for House Republicans to pass budget legislation that would defund Obamacare — forcing President Obama and Democrats to shut down government if they refuse to accept it. However well intentioned, this would be a disastrous strategy for Republicans to pursue.

Any strategy for resisting Obamacare has to recognize that Obama and the Democratic Senate will never, ever, pass or sign legislation that would undermine his signature legislative achievement. If Obama accomplishes nothing during his second term but ensure that his health care law gets implemented, he’ll look back on his presidency as a success for liberalism.

Arguing that there’s no way that Republicans can defund Obamacare without control of the Senate and presidency is not a defeatist attitude, but a recognition of reality. There’s a reason why it was important for Republicans to regain the Senate and win the presidency in 2012. They lost. This means they have the power to resist Obama, but not to effectively get rid of his crowning achievement by sheer force of will.

Saying that Obamacare won’t be repealed or defunded as long as Democrats control the presidency and Senate doesn’t mean that there will never be any opportunity for Republicans to make changes to the law. Should they regain power, and if Obamacare is the failure that many of us expect, there will be a chance for a future Republican Senate and president to re-open it to changes (though full repeal remains a remote prospect once people start receiving subsidies). To regain power, however, Republicans must get elected, and must make sure that the health care law remains unpopular.

There are a number of ways to go about this. One thing that the House has already done is focus on how the Obama administration delayed the mandate for big business to provide health insurance, while the individual mandate (promoted by the insurance industry) remains.

An idea I proposed is to use the budget battle to highlight the fact that the Obama administration delayed anti-fraud measures meant to ensure that hundreds of billions of taxpayer health insurance subsidies end up going to the right people. Rep. Diane Black, R-Tenn., subsequently sponsored legislation along these lines.

Americans don’t like Obamacare, but they don’t like government shutdowns, either. If Republicans force a shutdown of government over defunding Obamacare, then they risk making Americans feel as though opposition to Obamacare has gone to far. The defunding strategy had been described as some sort of last stand against the law, and it may very well end up being that. But the budget fight doesn’t need to be the last stand. It should be seen as another opportunity to highlight negative aspects of the law to maintain its unpopularity heading into its implementation next year, and to build political momentum for change in 2014 and 2016.