For the White House, the key to any deal is tax revenues -- delivered at least partly through higher rates -- and a long-term solution to the debt ceiling. Additionally, any big deal will have to include some stimulus, including an extension of unemployment insurance and either an extension of -- or more likely, a replacement for -- the payroll tax cut.

For Republicans, the key is some give on tax rates, as well as a few high-profile entitlement cuts, namely an increase in the Medicare eligibility age and chained-CPI.

It's by no means certain the two sides will come to a "grand bargain" before the end of the month. But if they do, the bargain will likely include either those policies outright, or instructions for Congress to work on those policies over the coming months.

But any deal will include much more than those top-line items. It will also include deficit-reduction and tax reform targets for Congress to hit in the coming months. That gets to a deeper problem in the negotiations: When you drill down to the granular policy level, Republicans aren't sure what Republicans want. Democrats complain that the Republican offers are bare of policy detail. They lay down targets -- say, $600 billion in health savings -- but say nothing about how those targets will be achieved.

Republican staffers admit that they need more time to come up with specific cuts -- and, for that matter, specific tax reforms. But they argue they'll have that time. Any deal is expected to include a two-stage process: Targets for spending cuts and tax revenues now, combined with consequences that force Congress to hit those targets later.

The administration is a bit agog at this approach: If you don't know how you're going to hit your target, how can you possibly know whether your target is reasonable? It's like buying a house with the expectation that you'll figure out how to pay for it later.

This is important context for the role the Medicare eligibility age is playing in these discussions. Though it's emerged, alongside chained-CPI, as the GOP's top ask in the negotiations, it's disconnected from any larger theory about how to slow the rise in health-care costs. There's no particular conservative -- or even non-conservative -- policy goal that raising the Medicare eligibility age advances.

Raising the Medicare eligibility age doesn't increase competition in Medicare, as some variant of premium support might. It doesn't reduce national health spending -- actually, as Medicare is cheaper than equivalent private insurance, it increases it. It doesn't force seniors to act as more discerning consumers of health care, as various forms of deductibles and co-pays might. It doesn't substantially pare back "the nation of takers," as many of the 65- and 66-year-olds thrown off Medicare will enter the exchanges or be caught by Medicaid.

And it shouldn't be forgotten: Raising the Medicare eligibility age really will hurt some seniors. The poorest seniors will be okay, thanks to Medicaid and the Affordable Care Act -- though that assumes that by the time the age increase phases in all states are participating in Obamacare's Medicaid expansion or that the deal includes some protection for seniors in states that have rejected it. Richer seniors will be fine, thanks to their wealth or to their employers. But there are a number of middle-income seniors who make enough that they won't get much help from Obamacare, who are sick enough that they won't get a good deal from insurers, and who may end up going uninsured (after paying the individual mandate's penalty) or straining under the cost of health insurance.

On Thursday, House Minority Leader Nancy Pelosi described the Medicare eligibility age as "a trophy that the Republicans want." That's exactly right. For Republicans, it's a signal that they won something big on entitlements. In a party that's confused about where to go on Medicare, it at least proves they're going in a direction Democrats hate.

The White House doesn't like the idea, but administration officials see its incoherence as a virtue. The reason it doesn't cut national health expenditures is that a lot of the pain is blunted by other players, like Medicaid and employers. The reason it doesn't significantly pare back the safety net is that Obamacare is law, and by the time these age changes phase in, it will be deeply entrenched law. Better to give Republicans a bigger trophy than a deeper cut, or so goes the theory.

But that gets to the real question: What will the rest of the package look like? While it's true that Republicans are confused on Medicare now, it's also true that they won't remain confused for long. As a plugged-in Republican policy wonk pointed out to me, the negotiators in the talks are mainly House Republicans, and they've sunk their energies into promoting premium support as the one and only Medicare reform worth doing. But among Senate Republicans, there's been a lot of work done on more piecemeal reforms, and soon enough, Republicans will begin working off of bills like Coburn-Lieberman or (the non-premium-support parts) of Coburn-Burr.

Progressives have reacted to the prospect of an increase in the Medicare eligibility age with fury. If that policy is included in the final agreement, then the White House is going to have to be able to persuade its base that the trophy of an increased Medicare eligibility age really did forestall much worse cuts in programs, and really did unlock more revenues and more stimulus than would've been available otherwise. The politics of that explanation are difficult, though, as it's tough to sell a deal in terms of what wasn't in it.

The cynic would say that the White House sees the fury of progressives as an inevitable byproduct of a deal. Even when the administration had large majorities, its legislative victories tended to end with progressive disenchantment. The stimulus was larded with tax cuts and reduced from an already too-small $900 billion to less than $800 billion. The public option was dropped as part of the cost of passing the health-care bill. The Bush tax cuts were extended as part of the cost of getting more stimulus in 2011. In each case, the final agreement infuriated many on the left.

The White House wants a deal. Administration officials want one because they think passing more stimulus and reducing the deficit is important, and they want one because they think the scheduled austerity would be devastating to the economy. They want one because a budget deal is a necessary precursor to moving onto other priorities like immigration reform, and they want one because a big budget deal is seen as a key element of the president's legacy.

The White House is firmer on its red lines in this deal than I can remember in any other negotiation. Administration officials don't want a deal so badly that they'll accept one that doesn't raise tax rates, or that leaves another debt-ceiling crisis around the corner. But if Republicans will give on those issues, the White House has always been clear that it is willing to put a lot on the table. "We’ve had conversations where [President Obama] told me he’ll go much further than anyone believes he’ll go to solve the entitlement problem if he can get the compromise," Sen. Tom Coburn (R-OK) told me back in May. "And I believe him. I believe he would."