Palin has now put the party in the position of having to choose between pushing for impeachment - a political loser likely to backfire - or disappointing the conservative base and appearing weak.
What is more, her comments invite every journalist in the United States to ask every Republican candidate running in 2014 the following question: "Do you support the calls for impeachment?"
Palin reaps the benefits and the costs are dispersed among her colleagues. But the problem for the Republicans is that it is not just Palin they have to worry about. There is an army of Palins now, each one playing this game, each to the collective detriment of their colleagues.
And so the Republican Party simply has to survive this death by a thousand cuts until November's elections - after which, presumably, it begins again.
The party's problems are merely a microcosm of much larger and disturbing trends in American public life. It has, for example, become almost de rigueur to call for the impeachment of a president whose policies you do not like and whom you cannot defeat.
Consider the fate of our modern Presidents since Richard Nixon was forced to resign. Henry B. Gonzalez, a Democrat from Texas, wanted the House of Representatives to impeach Ronald Reagan on two occasions: after the Grenada invasion and over the Iran-Contra affair. A poll of voters nationwide just ranked Reagan the best President since World War II, so we're lucky that didn't work.
There were calls for George W. Bush to be impeached over Iraq in 2006 - calls that had to be quashed by the leading Democrat Nancy Pelosi. She recently said she did not want to put the country through the turmoil, but one also supposes that at the time she wisely concluded it would distract from her efforts to retake the House that year.
And, of course, before Bush, Republicans actually did impeach Bill Clinton. It's worth mentioning that Republicans had a bad year as a result, while Clinton remained wildly popular.
The desire of sore losers to resort to legal process to nullify the will of the people is a bipartisan urge that should be discouraged. But it also makes perfect sense. We like our immediate gratification. Rather than taking our lumps, accepting defeat graciously, vowing to work together as a nation and redoubling our efforts to win the next election, the new instinct is, instead, to try to invalidate the last one.
Interestingly, we are no longer even waiting until someone is sworn in to begin the process. Thad Cochran won re-election as Mississippi senator weeks ago, but you wouldn't know it based on his opponent's behaviour. His conservative challenger, Chris McDaniel, is demanding that a new election be held because there were too many irregularities in the last one.
Now, one might applaud this American "never say die" spirit, but there are problems with it, including the fact that a society in which nothing is ever settled, and nobody ever accepts a loss, is in constant turmoil. This is the stuff of banana republics. There is also this inconvenient fact: merely impeaching Obama would not remove him from office anyway. He would be put on trial by the Senate, but the two-thirds majority needed to force him from the White House would be unattainable. And imagine the long-term optics involved in a Republican Party that chooses to impeach and attempt to utterly delegitimise the first black president.
This is not to say that I approve of all the President's policies. Palin's strategy and motives may be questionable, but I do not want to diminish the frustration many Americans have regarding Obama's tenure. His many failings include executive overreach, a disastrous foreign policy and a plethora of random scandals. But the notion of impeachment is a bridge too far. And the Republicans would be better off if Palin stopped sounding off about it.
Matt K. Lewis is a senior contributor at The Daily Caller website in Washington.