Right now, if Congress fails to come to an agreement on an overall deficit-reduction package by the end of the year, everybody's taxes will automatically go up on Jan. 1," President Obama explained Friday. "Everybody's -- including the 98 percent of Americans who make less than $250,000 a year. ... It would be bad for the economy and would hit families that are already struggling to make ends meet." Obama was describing the "fiscal cliff," over which he and other Democratic leaders have already said they would be happy to jump.

Republicans were elected to oppose Obama's agenda, and they should do so. But here is one fight where they would be mistaken to take a hard line. It is a trap, and they will only be playing into Obama's hands if they somehow convince themselves that they have much leverage.

Think about it for a moment. Let's say House Republicans adopt a no-compromise position and refuse to vote for anything that doesn't extend all current tax rates, including those at the top. America goes over the cliff. Tax rates rise on everyone. Defense sequestration kicks in. Markets panic. And then what happens? Simple: Obama comes back to Congress in January, asking for a retroactive cut in tax rates for families making less than $250,000.

What are Republicans going to do? Vote against a substantial tax cut and -- on top of being blamed for the standoff -- lose their brand as the tax-cutting party? Having already lost its edge with the public on national defense issues, the GOP cannot afford to lose its low-tax label as well. Republicans would have no effective argument to defend themselves from such a vote in the 2014 election. Legislative process arguments don't work, unless you think John Kerry was a genius for explaining that he voted for the $87 billion before he voted against it. Such arguments carry no weight. And even if they do try to stop a restoration of lower-bracket tax rates, there is no guarantee that Obama won't peel off enough House Republicans to pass his post-cliff "tax cut," either -- after all, it's not hard to get Republicans to vote for tax cuts.

If they take too hard a line here, Republicans will be shooting themselves in the head and getting nothing in return. They can, however, cash in Obama's promise during the presidential debates not to let the defense sequestration happen.

The House GOP majority was re-elected so that it could resist Obama's second-term agenda, but Republicans must pick their battles wisely. They will have legitimate leverage against Obama later on. Governors and state legislators should resist creating state insurance exchanges under Obamacare. Congressional Republicans may find themselves with even more leverage when Obamacare's implementation becomes a disaster and the law requires an overhaul. Even the next debt-ceiling fight will be an attractive battle compared with this one -- they might be able to extract concessions in the form of spending cuts.

But of all the fights that loom, this is not the one for Republicans to pick. It might seem like a bad way to start Obama's second term to give in, but the path of resistance here is a trap. Conservative voters must understand this before they reflexively push congressional Republicans off a political cliff.