President Obama has said health care is the next major item on his domestic agenda and that it remains a “year one” priority. But just how big are his policy ambitions? And how, precisely, does he intend to pursue them?

Answers to those questions will start to come this week, when Obama outlines his budget priorities in a speech and formal report to Congress. And while I don't know many details, I do have a rough sense of what's in store, based on multiple conversations with administration officials. 

According to these sources, Obama will restate his commitment to making health care available to everybody, to improving the quality of care, and to bringing its costs under control--in effect, reiterating the promises he's made since he started running for president. He will also call for putting aside money in the budget for fulfilling that commitment--a sum, I’m told, that will be “significant” and enough to convince skeptics he’s serious about the endeavor.

Some of that money will represent savings from other government health programs. For example, Obama will propose that the government reduce the excessive payments it now gives to private insurers participating in the Medicare program. Another source of funds will be a financial contribution from medium- and large-employers who don’t provide employees with health insurance.

But even when all of this money is put together, it won’t be enough to pay the very high cost of universal coverage. Making coverage available to everybody involves, among other things, expanding programs like Medicaid and subsidizing the purchase of insurance for people who can’t afford it on their own.* And although Obama will aggressively pursue reforms designed to make medical care less expensive over time,  it will be many years before those reforms can yield significant savings.

Here’s where things get interesting. Obama will say he’s determined to find that remaining sum, through offsetting revenue increases or spending cuts that will allow him to stay true to his pledge of fiscal responsibility. But Obama won’t be specifying the offsets in this budget overview. Instead, he’ll pledge to work with Congress on identifying them.

So...should advocates of universal health care be encouraged--or disappointed?

If Obama were absolutely committed to making health care affordable for everybody, one could plausibly argue, he'd set aside all the money for doing that now--even if it meant allowing higher deficits or proposing more taxes. But several health care advocates and experts have suggested to me that Obama might be making a smart strategic calculation here.

Obama would be foolish to sketch out a full financing scheme right now, they said, since it’d simply give critics a big target with time to take it down. Given that Congress has to write the bill anyway, it makes sense to let Congress take some ownership of the process and find the rest of the money--albeit with Obama's guiding hand.

(Bill Clinton's decision to nail down every detail in his health care proposal, instead of letting Congress take the lead, was arguably one of his biggest strategic blunders.)

Of course, it's hard to draw firm conclusions about Obama's judgment, substantive or strategic, without seeing the actual numbers. Just how big is Obama's initial budgetary allotment? How much do he and Congress sitll have to find?

But this much seems certain already. If Obama indeed intends to rely on unspecified fiscal moves to fulfill his vision of health care reform, it's important he use rhetoric to convey the depth of his commitment to making sure everybody has insurance.

That’s why the speech, which Obama delivers Tuesday night, is so crucial. It won’t have the charts, graphs, and figures of the budget overview the administration presents on Thursday. But it may have as much influence over the course of the debate.

*Update: I originally wrote "private insurance" but Obama has said--quite rightly--that it's also important to create a public insurance option into which anybody could enroll. Also, while the Obama administration will likely call for employers to contribute money if they don't provide employees with insurance, the money those contributions generate aren't part of this early budget allotment. 

--Jonathan Cohn