The single most important fact about the fiscal battles consuming Washington right now continues to be poorly understood. It’s this: Republicans are not going to get the serious entitlement cuts they say they want unless they agree to new revenues.

To put this in another way, there is no imaginable scenario in the next three years, and probably beyond, under which Republicans win a total victory. Obama and Senate Dems will never agree to a fiscal deal that achieves the remaining deficit reduction experts have called for with only spending cuts, including serious cuts to retirement programs. There’s actually precedent for trying this: In 2005, President Bush and Republicans tried to enact a massive plan focused only on reforming entitlements. Even though Bush was riding high after reelection — and Republicans controlled both houses of Congress — the whole effort collapsed in abject failure, with even GOP officials running away from it. So, no, there won’t be any entitlement-reform-only package anytime soon.

Here’s why this is key to the current battle. It leaves only two possible conclusions: Either the two sides reach a deal that combines serious entitlement cuts and new revenues via the closing of loopholes, or there is no deal and the sequester continues indefinitely.

It is plainly obvious that the former outcome is far better for not just Dems, but Republicans, too. This is the operating premise behind the White House’s new strategy of reaching out to GOP Senators who may be open to a revenues/cuts deal. Even if the GOP leadership is entirely entrenched in its no-revenues stance, sooner or later, the basic reality of the situation will become impossible for other GOP lawmakers to fail to acknowledge. These lawmakers have ducked this reality by taking refuge behind a party-wide distortion (Obama only wants more tax hikes!) of the actual compromise Obama is offering.

But the White House’s new outreach strategy is making that position harder to sustain. Via Steve Benen, consider this remarkable tidbit from First Read’s write-up of yesterday’s Obama dinner with Senators: “one senator told us that he learned, for the first time, the actual cuts that the president has put on the table. Leadership hadn’t shared that list with them before.”

There will be a lot more of this, as more GOP officials acknowledge what it is they’re actually being offered. This dynamic could be hastened if the pain of the sequester starts to be felt in individual districts and states, thanks to defense and other cuts, focusing the minds of the lawmakers who represent them. And there actually is a (difficult) route to a place where enough non-leadership Republicans agree to a deal. As Noam Scheiber details in a must read, this could happen even if GOP leaders publicly oppose such a deal while tacitly understanding that it’s the best way out for everyone and allowing it to happen.

There is only one alternative to that conclusion, short of the GOP taking back the White House and Senate, and trying another entitlements-cuts-only package (an extreme long shot scenario at best). It’s continued sequestration. While GOP operatives can tout this or that poll supposedly showing they have the upper hand, the big picture is that continuing down this path means only one thing. As Bloomberg News describes it, sequestration with no end is a trap, one that offers only “the pain of economic austerity without the gain of addressing the long-term budget gap.” Even if you grant that Obama will take a political hit in this scenario, he isn’t up for reelection, and Republicans — who are up for reelection — certainly will take a hit, too. At bottom, it simply isn’t a sustainable long-term position for anyone. Even more to the point, there is only one plausible way out of it: A deal that combines new revenues with serious entitlement cuts.

The ultimate irony in such an outcome is that Republicans could plausibly declare victory. If they accepted Obama’s current offer as is, that alone would amount to a short term victory, since it contains far more in spending cuts (over $900 billion) than new revenues (nearly $600 billion). According to Paul Van de Water of the Center on Budget and Policy Priorities, this would mean that overall, we would have achieved nearly $4 trillion in deficit reduction, through a cuts-to-revenues ratio of 1.8 to one — nearly $2.5 trillion in cuts, versus nearly $1.4 trillion in revenues — after Obama decisively won an election about these matters. Republicans could say they forced Dems to accept entitlement cuts and got significantly more in cuts than they gave away in revenues.

If Republicans really want to tackle the deficit, they just have to accept Yes for an answer.