After 2½ years of budget battles, the U.S. federal government is on pace this year to spend $3.455 trillion.

That figure is down from 2010 — the year that worries about government spending helped bring on a tea party uprising, a Republican takeover in the House of Representatives and then a series of showdowns in Congress.

But it is not down by that much. Back then, the government spent a $3.457 trillion.

Measured another way, the government has about 4.1 million employees today, military and civilian. That is more than the populations of 24 states. Back in 2010, it had 4.3 million.

Today another budget fight looms. If Republicans and Democrats can’t agree on spending levels by Oct. 1, there could be a government shutdown — followed, perhaps, by a national credit default.

That will be showdown No. 7. To assess what the first six accomplished, The Washington Post tried to measure the government in four dimensions: expenditures, workers, rules and real estate.

The first two were down, slightly. The third was way up. And in the fourth case, the government itself wasn’t sure what happened.

In every category, there was evidence that — even as politicians made some headway in reducing the budget — they could not shake many of the old habits that made government big in the first place. They allowed duplication to live. They let “temporary” giveaways turn permanent. And they yielded to inertia, declining to revisit expensive old decisions.

The result was that Congress often passed up “smart cuts” in favor of dumb ones — taking broad hacks at the budget, instead of pruning away what was unnecessary.

“For all the brave talk, one single fact has trumped all this great rhetoric. Most of the people who came in saying, ‘We’re going to change Washington’ simply didn’t understand Washington,” said Steve Bell, a longtime Republican staffer who now works at the Bipartisan Policy Center.

Bell’s point is that today’s politicians do not understand the political forces that produce and then protect inefficient programs. Or the difficulty of changing the social-benefit programs — such as Medicare and Social Security — that spend the bulk of Washington’s money.

“That kind of hard-edged budget work . . . is just too complicated. And just too politically incendiary, for this town to do,” Bell said. “That’s why this town hasn’t done it.”

The reduction in federal spending since 2010 is still something historic. — any reduction in spending would have been, after a decades-long spending binge that peaked in the first years of President Barack Obama’s term.

This year, the government’s spending is projected to be down by about 5 percent from 2010, accounting for inflation.

But even now, the government still spends a vast amount of money.

This year’s projected spending will be more than in any year of the George W. Bush administration, and more than 30 percent higher (accounting for inflation) than the last year of President Bill Clinton’s term.

It is still so big primarily because Congress and Obama have largely failed to deal with programs such as Medicare, Social Security and food stamps.

These “mandatory spending” programs are very large, accounting for about 60 percent of federal spending. Congress doesn’t set their spending every year. Instead, when need goes up, spending goes up. And, in the recession, need went up.

Even after six paralyzing budget showdowns, this “mandatory” spending has fallen by less than 1 percent. By contrast, spending on “discretionary” expenses — the smaller pot of money that Congress does control every year — has fallen by 14 percent. That reduction is partially due to the winding-down of a stimulus and two wars, as well as to “sequestration” and other budget cuts imposed since 2010.

“We’re nowhere. I mean, the sad reality is that we’re nowhere” toward taming those “mandatory” costs, said Gordon Adams, a budget official in the Clinton administration.

And now, in a capital burned by six crises, a deal to cut these big-ticket programs seems less likely than ever. “We’ve gotten further away from anything that will bring us to a ‘grand bargain’ right now,” Adams said.

But it is not only the big cuts that Congress has struggled with. It has also found it hard to break several little bad habits that made government fat in the first place. One is pork, the habit of using taxpayer money for a legislator’s pet cause.

Today, its power appears to be stronger even than death.

That is clear from the story of the Robert C. Byrd Highway, a decades-old road project in West Virginia that had received earmarked funds for years from Sen. Robert Byrd, a West Virginia Democrat, the longest-serving senator in history, who died in 2010. The highway has been maligned as a wasteful road to nowhere. But, now, it has outlived earmarks. It has even outlived Byrd. This year, with continued support from Sen. John Rockefeller IV, a fellow West Virginia Democrat, the highway got $40 million in federal money. It will need about that much every year, state officials say, until it is finished in 2035.

This Congress has also indulged in the habit of letting “temporary” giveaways become effectively permanent.

A prime example is the Essential Air Service, a $240 million program that subsidizes flights to 161 small airports. It was supposed to die in 1988. It didn’t. Congress has renewed the program again and again. Now it subsidizes flights to places such as tiny Glendive, Montana, where the government pays for a 19-seat aircraft to visit twice a day. On average, two people get on each day. The subsidy works out to $836 for each ticket.

“If we can’t cut this, we can’t cut anything,” said Rep. Tom McClintock, a California Republican who sponsored an attempt to kill the program last summer.

McClintock’s amendment lost by 74 votes. Then he tried again this summer. And lost. Many members explained their “no” votes by saying they were unwilling to sacrifice the subsidies to airports in their districts.

“It’s that old problem of concentrated benefits with diffuse costs. The benefits are lavished on a few select communities, and the costs are diffused across the entire tax base,” McClintock said afterward. The beneficiaries, he said, are the only ones who care enough to fight.

Still, McClintock says he is holding out hope. After all, the first time he got 164 votes in favor of this cut. This year: 166. He needs 218 to win.

In terms of people, the federal government is smaller by about 170,000 employees. In many cases, the reductions came as employees left and cash-strapped agencies could not afford to replace them.

Today, the government workforce includes 2.7 million civilian employees, including postal workers — a number that is roughly equal to the population of Nevada. It also includes 1.4 million active-duty members of the military. That is roughly the population of Hawaii.

But those numbers are still incomplete. They do not count a vast number of other people who also do the government’s work: private contractors who do federal work full time.

It is hard to judge the actual size of the government — or the actual scope of its work — without knowing how many of these people exist.

The Obama administration doesn’t. It was supposed to have started counting these contractors: Congress ordered it in 2009.

But the formal regulations haven’t been finalized. So there is still no full count. There are only educated guesses.

The trade association for federal contractors, for instance, guesses the number may be about 1.7 million full-time contractors. That would make the actual size of the federal workforce 5.8 million people — more than the populations of 31 states.

Another way to measure the government’s size is by the length of its rule book, the Code of Federal Regulations. It is now as long as 95 King James Bibles.

This code book had always been a living example of government inertia. Time went by, rules went up.

He announced a “regulatory lookback” to eliminate unnecessary rules. A few got the ax. The administration cited five examples. one of them, dating to the 1970s, mandated that a milk spill should be treated as an oil spill.

But the book kept growing. In all, the Code of Federal Regulations has grown by 16,500 pages under Obama.

Finally, the government can be measured in buildings. At last count — in 2010 — the federal government had about 399,000 of those. Inside them was enough space to cover the District of Columbia twice over with cubicles.

Not all of it was actually needed. In 2010, the government’s 6,700 unused “assets” contained 18 million sq. meters of space.

So how much space is sitting empty now? The government can’t say. Officials can cite examples of unneeded buildings that it has gotten rid of. An old heating plant in Washington was sold for $19.5 million. A navy warehouse in Brooklyn, New York, went for $10 million. But what is the total?

“No public update at this time,” a federal spokesman said.

One reason the government stakes out so much office space is the common federal government practice of duplication. That is when two arms of government — sitting in two different places — do the same job at the same time. Or three arms. Or four.

Or 226: The administration now counts 226 separate programs that aim to promote education in the “STEM” fields: science, technology, engineering and math. Many overlap, according to outside audits. Some overlap substantially. This year, the administration proposed to consolidate them in the name of efficiency. The number should shrink, they said — all the way down to 110.

Elsewhere, the Obama administration has managed to pare down other duplicative programs. It closed more than 484 unneeded data centers and actually reduced the number of employee email systems in use at the Department of Agriculture to one — down from 21.

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