Republican lawmakers - led by Tea Party favorite Sen. Mike Lee of Utah - are threatening to shut down the government if Obamacare is not defunded. While the timing is perfect, conservatives can (and are) debating the overall strategy.

On Sept, 30, 2013, the federal government's fiscal year comes to a close - and with it the Continuing Resolution that provides its funding. To keep things running, lawmakers in the House and Senate must either pass a budget or another CR to provide funding for existing government programs at current, reduced, or increased levels.

Without funding, discretionary spending - such as funding the National Institutes of Health - would be hit first. Major categories of mandatory spending such as Medicare and Social Security (which rely partly on trust funds) would continue to pay existing bills and send out checks, while new claims would take a backseat.

But, though this may seem to be the perfect time for the GOP to take a hard-nosed stand against Obamacare, Republican lawmakers would do well to think carefully about the most likely scenarios associated with a de-funding strategy.

For starters, Republicans took most of the blame for the government shutdown of 1996, ensuring President Clinton's reelection. Would this time be any different? While Obamacare may not be a popular law - indeed, more than half of likely voters view the law negatively - the prospect of shutting down the government is viewed even more negatively, with 64 percent of likely voters opposing it. Polls from the near-shutdown in 2011 tell a similar story.

That's not all, though. A shutdown may not actually defund Obamacare - at least not initially. That's because most of Obamacare's funding is mandated by existing legislation.

As the Congressional Research Service noted recently: "[S]ubstantial [Obamacare] implementation might continue during a lapse in annual appropriations." Simply put, subsidies and spending would continue to flow.

But there's an even more important point that supporters of the "defund-Obamacare-or-else" movement seem to be ignoring. The president and congressional Democrats will never agree to it. They will fight bitterly to defend their signature legislative achievement.

If Republicans truly dig in their heels on defunding Obamacare, the U.S. may very well experience a government shutdown. This would likely last no more than a week or two, after which lawmakers would agree on a new CR.

Then again, Republican lawmakers might cave before a government shutdown and sign a CR. Both scenarios bode poorly for the GOP - the first makes them appear irresponsible and overreaching, while the second makes them look weak.

Rather than pursue what could be best described as an "all or nothing" strategy where anything short of complete defunding is defined as failure, the GOP should take House Speaker John Boehner's advice to focus on "targeted strikes" against the health care law.

This strategy has been somewhat successful so far, resulting in the repeal or delay of some of Obamacare's more odious requirements. Building on this strategy means directing legislative attention toward remedying the very real flaws in Obamacare - loosening or repealing age-rating bands; eliminating the employer mandate; and lowering the subsidies to high-income families.

Defunding Obamacare sounds great in theory - as does the argument that Republicans have failed to repeal it due to a lack of conviction. In reality, they continue to control only one-half of one-third of the three branches of government, and have just lost - decisively - a presidential election.

A defunding strategy that fails is not only counterproductive, but would set back further attempts to reform and ultimately replace Obamacare.

Yevgeniy Feyman is a research associate with the Manhattan Institute.