For instance, they'll advocate one of their policies by saying:
Even my opponent supports my position on this issue.The implicit argument is that -- since political opponents usually disagree on things -- when they reach consensus and agree on some position, that position must be correct. (The Latin name for it I suppose would be argumentum ad hostes.)
But this is flawed reasoning. Is it impossible that two political opponents could both be wrong at the same time? What's preventing that? Nothing.
Just because your opponent supports the same position you do doesn't somehow give that position extra credibility.
Bipartisanship is often praised using the same flawed reasoning: if opposing parties are agreeing on something, they must be right about it.
This is an instance of a particular kind of fallacious reasoning, the appeal to authority.
EXAMPLES AND ANALYSIS
TEXT: Republicans keep saying the same thing.-- Democratic Party political ad, retrieved November 24, 2015. The ad quotes Republican presidential contenders former Gov. Jeb Bush (R-FL), Ben Carson, Sen. Ted Cruz (R-TX), Sen. Marco Rubio (R-FL), and Donald Trump, as well as former President George W. Bush.
RUBIO: We are at war with radical Islam.
JEB BUSH: Radical Islamic terrorism.
TEXT: Equating Islam, all Muslims, with terrorists…
TRUMP: We do have a problem radical Muslims.
CARSON: Radical Islamic jihadists.
CRUZ: Radical Islamic terrorism.
TEXT: It’s oversimplification. And it’s wrong. But don’t take our word for it.
GEORGE BUSH: We do not fight against Islam, we fight against evil.
GEORGE BUSH: The war against terrorism is not a war against Muslims, nor is it a war against Arabs. It’s a war against evil people who conduct crimes against innocent people.
GEORGE BUSH: That’s not what Islam is all about. Islam is peace.
TEXT: Inciting fear isn’t presidential.
Comment: The ad is accusing Republicans of fear-mongering. It is also falsely accusing Republicans (perhaps via code words?) of equating Islam and Muslims with terrorism and terrorists, thereby demonizing them as bigots. Being opposed to radical Islam doesn't mean being opposed to all Muslims, any more than being opposed to corrupt police officers means being opposed to all police officers. Citing George Bush – a Republican – seems like a faulty appeal to authority, perhaps an argument ad hostes. (Plus, the ad cites George Bush selectively: he denounced Islamic radicalism.)
Apparently, he thinks there’s nothing amiss in suggesting that the only thing standing between the present moment and the broad, sunlit uplands of a denuclearized Iran is the Jewish state and its warmongering Beltway lobbyists. That slur in particular was the loudest dog whistle heard in Washington since Pat Buchanan said in 1990 that the Gulf War —advocated by columnists like Abe Rosenthal and Charles Krauthammer—would be fought by “American kids with names like McAllister, Murphy, Gonzales and Leroy Brown.” Then again, Mr. Buchanan wasn’t the president. It says something about the crassness of Mr. Obama’s approach that the New York Times noted that allies of the president fear he “has gone overboard in criticizing” opponents of the deal. But it also says something about the weakness of his deal.-- Pundit Bret Stephens, August 10, 2015. Stephens' remarks refer to President Barack Obama.
Comment: Stephens is accusing Obama of using "code words". He is also arguing that, since even Obama's allies (who are Stephens' adversaries) are criticizing Obama's rhetoric, therefore the criticism is credible, which is flawed "even my opponents" reasoning.
RUSH: Here's Ken in Miami. I'm glad you waited, sir. Great to have you on the program.-- A caller to the Rush Limbaugh show, June 1, 2015.
CALLER: The reason I called was that Republicans were elected to stop Obama. Obama publicly endorsed the USA Freedom Act, so shouldn't that be enough for the Republicans to be against it?
RUSH: Yeah. I feel your pain. The Republicans even acknowledged that they were elected to stop Obama, but then when they have the chance, they don't. Like in the trade deal. This transpacific partnership that still remains a big mystery. It's the Republicans that are gonna pull Obama -- it's caused me to be on the same page as Elizabeth Warren on this. Imagine how bad this thing must be. Actually, Elizabeth Warren's on the same page with me on this thing.
Comment: The caller is saying Republicans have a mandate to stop Obama – or, perhaps, that they have not mandate to NOT stop Obama. The caller also argues that Obama's support for the USA Freedom Act is cause to oppose it, which is something of a reverse appeal to authority (and still invalid reasoning). Limbaugh notes that he agrees with his opponents on the transpacific trade deal, but doesn't seem to use that as an "ad hostes" argument.
Examples from 2012.
Examples from 2011.
"All Government employees should realize that the process of collective bargaining, as usually understood, cannot be transplanted into the public service. It has its distinct and insurmountable limitations when applied to public personnel management. The very nature and purposes of Government make it impossible for administrative officials to represent fully or to bind the employer in mutual discussions with Government employee organizations. The employer is the whole people, who speak by means of laws enacted by their representatives in Congress. ... Since their own services have to do with the functioning of the Government, a strike of public employees manifests nothing less than an intent on their part to prevent or obstruct the operations of Government until their demands are satisfied. Such action, looking toward the paralysis of Government by those who have sworn to support it, is unthinkable and intolerable."-- President Franklin Delano Roosevelt (FDR), August 16, 1937, letter to Luther C. Steward, then President of the National Federation of Federal Employees.
Comment: FDR's position here -- that public sector unions should not be allowed to engage in collective bargaining -- was frequently cited by Republicans and conservatives who were supporting the restriction of collective bargaining rights for public sector unions in Wisconsin in 2011. Many liberals, progressives, and Democrats opposed this restriction, which was pushed by Gov. Scott Walker (R-WI). FDR was a Democrat, and his agreement with Walker and Republicans on this matter was offered as evidence that such restrictions were OK (in other words, committing the "even my opponents agree" fallacy).
(The list above is not intended to be a comprehensive record of all relevant examples.)