This is one of the weirder arguments I have heard recently. Making the case, I think, for the Romney/Ryan ticket, Ramesh Ponnuru argues thusly:
In the same AP interview, Obama suggested that Republicans would feel pressure “to cooperate on a balanced package” on the budget: that is, one with tax increases. Republicans famously failed to react to their drubbing in 2008 — after which, let’s recall, Time magazine was running cover stories on their impending extinction — by softening their line on anything. Why would they react that way after an election that goes better for them? Especially when they will be looking forward to the gains that the party out of the White House typically makes in midterm elections.
So the thought goes something like this. Republicans are rigid ideologues who will not compromise with the President. They remain so even when their views are unpopular. We have no choice but to vote for them if we want anything done. I must be getting this wrong, because that's asisine.
No, you have it correct, unfortunately. Alas, that's been the Republican Party's implicit or explicit argument since Obama's election, probably most evident with the debt ceiling "hostage" situation (made much more rigid by the Norquist pledge). Broadly speaking, the Republican approach was rejected by voters in 2006 and 2008, but Republicans still argued that America was/is a "center-right" nation and their electoral defeat meant – they had a mandate, and Obama had to bow to it. A few recent articles have given new detals about the Republicans meeting and vowing complete resistance to Obama from they very start, which would also (they thought) deny Obama any cover of "bipartisanship." (Lazy press coverage helps.) Unfortunately, there is a decades-old conservative tradtion of viewing any Democratic victory as inherently illegitimate. (Jesse Helms threatening Bill Clinton with physical harm if he came south, authoritarians who cheered on Bush's use of state power suddenly yelling about the evil Obama would do with the same power, etc. With a more racial tinge, there are the accusations that Obama is a Muslim and born in Kenya, that ACORN stole the 2008 election, and so on. Rush Limbaugh actually claimed someone else wrote Obama's student papers, one of his more bizarre attacks. With resentment comes rationalization, I guess.)
Of course, assuming the Republican policies are some mix of objectionable, irresponsible, reckless, etc. there is no beneift to giving them power. Some routine functions might get "done," but that's about it.
Atrios has called their stance (rightly, I'd say) hostage-taking (similar to your post title), and Echidne also wrote on this:
http://echidneofthesnakes.blogspot.com/2012_09_02_archive.html#5326246614956113290
As she notes, one alternative is to elect Dem majorities in both houses.
As Digby has often pointed out, the conservative base believes that conservatism cannot fail, it can only be failed. It's unlikely that a 2012 defeat will change that, unfortunately.
Sorry, my comment goes far beyond the illogic of the argument, but I think this is one of the instances where the illogic can only be fully explained with some of the psychology behind it. I'm not sure Ponnuru is a true believer (although he did write a book calling the The Party of Death, so he's not the voice of sober reason), but his entire piece does reflect the attitude that the Republicans do not need to compromise at all (and that there will be no or few negative consequences for this). What he's pitching – and you will see some 'sensible centrist' pundits actually pitching this as well – is that the Democrats should completely capitulate. It's all rather sad.