This Tuesday, the Obama administration will unveil its eighth and final budget proposal, its last comprehensive, detailed vision of how the federal government should look.

The budget is a key indication of the administration's values and priorities. It's an expression of the mainstream of Democratic Party policy thinking on a wide range of topics, from pre-K to housing to unemployment. Even though it has virtually no chance of changing actual government policy, that role is important in and of itself.

The wish list is expected to be relatively small-bore. It won't contain a sweeping single-payer health care reform (or even a public option), but it might offer small changes to the administration of Obamacare. It won't offer free college but might seek more accountability for for-profit colleges thought to be scamming students. It won't offer government jobs to the long-term unemployed, but it'll probably ask Congress to enact a wage insurance plan.

This pragmatic vision betrays a tension in the Democratic Party. While mainstream Democratic politicians are concerning themselves with fairly modest, practical policy ideas like those in Obama's budget, Democratic primary voters are flocking to Bernie Sanders's ideas, which are just as unlikely as Obama's to be enacted but also offer sweeping, ambitious changes to public life.

Here's what's actually going to happen to taxing and spending this year, what role the budget will play, and why you should be paying attention.

How the budget is supposed to work

To understand the budget process, you need to know the difference between budget resolutions and spending bills (or appropriations bills). The distinction might seem pedantic, but it helps explain why passing a "budget" is less important than it may sound.

Budgets don't actually allocate funding to specific government agencies. Indeed, budgets aren't even laws; they're "concurrent resolutions" agreed to by both houses of Congress but never signed by the president. They're simply deals that the Senate and House make with each other laying out how much money they expect to spend in a given fiscal year, category by category. To actually spend money, Congress has to pass spending bills that allocate money to various parts of the government per the parameters laid out in the budget they settled upon.

So budgets are mostly a tool Congress uses to keep its taxing and spending on track. The Congressional Budget Act of 1974 gives members of Congress the power to challenge any spending or tax bills that run afoul of the agreed-upon budget. This is mostly meaningless in the House, since it requires a simple majority of the House to beat back such a challenge (and you presumably have a majority if you're going to pass any budget-defying bills in the first place), but in the Senate, where 60 votes are required, it makes it hard to break with the budget agreement.

In addition to those powers, the Budget Act lays out a specific process and timetable that the president and Congress are supposed to follow when passing budgets and spending bills:

The president submits his budget request by the first Monday in February. The Senate Budget Committee then passes its own budget resolution by April 1. The Senate and House agree upon a budget, and pass the newly agreed upon plan, by April 15. The House Appropriations Committee passes all appropriations bills laying out how the money allocated in the Senate-House budget resolution will be spent by June 10. The Senate and House agree upon compromise appropriations bills and pass them all by June 30. The new fiscal year begins October 1, with all spending decisions made three months earlier.

How budgets actually do work

This, suffice it to say, is not how things normally work, particularly under divided government. For starters, the president's budget request is coming out eight days later than it's supposed to. But even once the president submits his proposal, there's little chance the Senate and House will agree to a budget before April 15, and even less chance they'll pass all appropriations bills by June 30.

From 2011 through 2014, when the Senate was under Democratic control and the House under Republican control, Congress didn't agree to any budget resolutions at all. Last year, the Republican Senate and Republican House actually did come to a budget deal, but the Senate only passed it on May 5, weeks after the supposed deadline.

And even though that budget passed, it didn't affect actual government spending. That's not surprising if you look at the actual content of the budget, which repeals Obamacare and slashes programs for people with low-incomes by 39 percent, among many, many other spending cuts. Actually doing that would require passing spending legislation implementing the budget, and that legislation would be vetoed by Obama.

Instead, what happened was that the 2014 spending deal reached by the White House and congressional Republicans lasted until the end of fiscal year 2015, on September 30. It was temporarily extended through December 11 and then again to December 16 and then again to December 22, but by December 18 Obama and House Speaker Paul Ryan had reached a spending deal that swiftly passed Congress and funds the government through September 30, 2016.

And throughout those negotiations, the boring budget process has been constantly upended by the threat of a government shutdown, with members of what now calls itself the Freedom Caucus trying to exact concessions on debt or defunding Planned Parenthood.

The ultimate deal reflected basically nothing in the budget to which the House and Senate agreed in May.

It's reasonable to expect something similar to happen this year. The president will lay out his agenda in his budget request. The Senate and House Budget Committee will lay out theirs in their own budgets. Because those budgets will be very similar to each other, there's a decent chance the two houses of Congress will agree to a joint budget that they'll both pass like they're supposed to (though they'll disagree on some things, so it's not inevitable an actual budget will pass).

But ultimately, current spending patterns will probably persist until September 30, unless the White House and Congress reach a spending deal lasting beyond that some time before that deadline. Newly elected Speaker Paul Ryan has already begun trying to head off a disastrous GOP rank-and-file revolt that would prevent such a deal, saying in a speech to the Heritage Foundation:

What I want to say to you today is this: Don’t take the bait. Let’s not fight over tactics. And don’t impugn people’s motives. It’s fine if you disagree. And there’s a lot that’s rotten in Washington -- there’s no doubt about that -- but we can’t let how someone votes on an amendment to an appropriations bill define what it means to be a conservative.

Ryan has indicated that he hopes to wrap up the process in July before August recess, but there's still resentment brewing. David Brat, a member of the Freedom Caucus who ousted former Majority Leader Eric Cantor in a surprise primary upset, said recently: "What good is it to be in the majority if we don’t act like it?"

So why should we care?

The budget proposal process is still important, even though it has basically no effect on actual government spending. That's because it offers both the president and the Senate/House Republican leaderships opportunities to lay out their blue-sky vision for what the American government should look like, and those visions can take on great importance over time.

Take pre-K, for example. Ever since 2013, the Obama administration has been including a proposal to expand access to preschool for low- and middle-income families in its budget, financed through a cigarette tax. That proposal never passed, and it's not likely to pass with the most Republican Congress Obama has faced at any point in his presidency.

But it did help make pre-K a core part of the Democratic policy agenda in a way it hadn't been before Obama's plan came down. At the time, it led to legislation in the House and Senate spearheaded by Rep. George Miller (D-CA) and Sen. Tom Harkin (D-IA), both of whom were the top Democrats on education in each chamber but who have both since announced retirements. Hillary Clinton's campaign promises that their preschool efforts will "build upon President Obama’s Preschool for All proposal." The proposal had influence merely by being a proposal put forth by the president, irrespective of its actual odds of passage.

An even more dramatic case is that of the Ryan budget. Starting in 2007, when he became the ranking Republican on the House Budget Committee, Ryan started putting together budgets that laid out comprehensive conservative plans for reshaping the federal government, slashing spending and instituting big entitlement reforms.

His first plan fully privatized Medicare and Medicaid, partially privatized Social Security, dramatically cut income taxes by setting brackets of 10 and 25 percent, eliminated the taxation of capital gains and dividends, abolished the corporate income tax and estate tax, and instituted a 8.5 percent value-added tax (VAT). The details changed over time (Social Security privatization, capital gains tax elimination, and the VAT got dropped, and the Medicare reform got less ambitious), but it still called for block granting and cutting food stamps and Medicaid, partially privatizing Medicare, establishing the 10 and 25 percent rates, and so on.

The Ryan budget, over time, came to be the definitive statement of Republican economic policy. It was the key reason Mitt Romney selected Ryan as his running mate in 2012, and why so much of that election focused on Romney and Ryan's plans for Medicare. Without the Ryan plan, it's doubtful he'd be speaker of the House right now, and it's doubtful that then-Speaker John Boehner and Majority Leader Eric Cantor would've pushed to make the 2011 debt ceiling deal as aggressive as it was. Ryan's budget never passed, but it changed history anyway.

Now, ironically, Ryan is in the position of making the deals rather than presenting an idealistic vision of conservative government. How he handles this process will be the first real test he'll face of transforming his vision into practice — and whether he can convince members of the Freedom Caucus to come along.

So pay attention to Obama's budget on Tuesday, and those of Senate Budget Committee Chair Michael Enzi and House Budget Committee Chair Tom Price when they arrive. They won't change policy in the near term, but they definitely matter.