One remarkable thing about the battle over Paul Ryan’s new budget — and the larger agenda it represents — is how utterly convinced both sides are that it plays in their favor.

Now that Ryan has endorsed Mitt Romney, the DNC is circulating a new Web video highlighting their closeness and Romney’s full-on embrace of Ryan’s Medicare and fiscal agenda.

But Republicans don’t see Ryan as a liability in any way. The Romney campaign just circulated a quote Ryan gave to a Wisconsin radio station that doubled down on just how tight they are with each other on economic matters. Ryan confirmed that both men’s staffs have been consulting with each other for weeks over their respective fiscal plans:

“Who has the best chance of winning the presidency? I think that’s Romney. Here’s why: I spent a good deal of time with Mitt Romney and his staff over the last number of weeks going through the kind of problems we have in this country. The fiscal problems, the economic problems. And just what it’s going to take to get this country back on track next year with a new president, new Senate and a House. And I’m convinced he’s got what it takes to do this. Now here’s why: we need to go the country with a real sharp contrast … from which to choose. We can’t just run against Obama and win by default.”

Now, obviously this is happening in the context of GOP primary politics: The Romney campaign is eager to advertise Ryan’s testament to Romney’s fiscal seriousness to end the GOP nomination battle.

But it goes well beyond this. Romney and other Republicans have fully embraced the Ryan agenda as their main offering in the great argument that will decide the general election and future direction of the country.

As my Post colleague Jennifer Rubin put it recently, Romney’s embrace of Ryan underscores the “degree to which the GOP is united on a bold reform agenda.”

I’m sure Dems would wholeheartedly agree.

Ryan fires up the base on both sides like nothing else, which is why Republicans like Romney want him in the role of hero, and Dems want him in the role of villain. But what about swing voters? Dems seem confident that the Ryan vision is absolutely toxic among them. And yet, as Jed Lewison notes, Republicans seem equally confident that Ryan’s radical vision — or “bold,” if you prefer — is a political winner this fall.

Nonpartisan observers say Ryan’s plans amount to a huge giveaway to the rich at the expense of exploding the deficit. Polls suggest that huge majorities favor preserving Medicare’s traditional function, and reject Ryan’s reforms. And yet the amount of influence Republicans have accorded to Ryan over the GOP’s fiscal policies, worldview, ideology, vision, priorities and direction is really kind of extraordinary. They’re going for it.

Update: Link to Tax Policy Center analysis fixed.