The late Sen. Daniel K. Inouye, who lost an arm fighting in World War II, once observed that advances in transportation and medicine were allowing soldiers to survive battlefield wounds that would have been a death sentence during his time in combat.

“In my case, it took nine hours to evacuate me. Nine hours? That is a long time. But in Italy, they have hills. We had no helicopters in those days. You had to be carried by hand. As a result, no brain injuries survived and no double amputees survived,” the Hawaii Democrat said in a 2010 floor speech.

Now, advanced treatment on battlefields followed by quick transport to more sophisticated medical care has shifted the odds of survival in war zones. The military has treated some 40,000 survivors with severe to moderate brain injuries suffered in connection with the wars, according to the Congressional Research Service.

The near-miraculous interventions that have spared many lives have also strained the resources of veterans health services and the ability of service providers to manage both the rehabilitation and the years of continual support that have grown out of wars in Iraq and Afghanistan. Added to this is the widespread post-traumatic stress disorder reported by veterans — the grim echoes of a decade of war.

“As we engage in wars, it is a two-part cost. One is the action of the war and the actions after,” said Sen. Mark Begich, an Alaska Democrat, at a 2011 Senate Veterans’ Affairs hearing. “When we engaged in the wars of Iraq and Afghanistan, not a lot of people thought about the next cost.”

By late 2012, about half of returning veterans from these conflicts — 783,623 of 1.66 million — had applied for disability benefits, according to a Department of Veterans Affairs document cited by Linda J. Bilmes, a budget expert at Harvard University’s Kennedy School of Government who wrote a book examining the costs of the Iraq War — “The Three Trillion Dollar War” — with Nobel Prize-winning economist Joseph E. Stiglitz in 2008.

The impact will reverberate on U.S. spending for many years, according to Bilmes.

“The legacy of decisions taken during the Iraq and Afghanistan wars will dominate future federal budgets for decades to come,” Bilmes said in a March 2013 paper on the costs of the two conflicts.

The cost of veterans care is only a fraction of that. Bilmes estimates the two wars will cost the United States $4 trillion to $6 trillion, with a variety of expenses including interest on the debt used to fund military operations and the replacement of equipment used abroad. She puts the costs of the future medical care and disability benefits for the Department of Veterans Affairs at a total of $707 billion within 40 years, with the costs of caring for veterans rising as they age.

With its expanding spending, the VA is an outlier in this time of tight budgets and is likely to be so for years to come. Veterans benefits were not subject to the sequester in the current fiscal year, and annual spending for the VA is on track to nearly quadruple from $45 billion in fiscal 2001, the last full budget year before the start of the war in Afghanistan, to $170.9 billion in fiscal 2018, according to Office of Management and Budget data. The VA share of federal operating expenses, or discretionary outlays, is likely to grow by more than half to 3.8 percent, as budgets on many domestic programs shrink by this measure.

The House in June passed, 421-4, a fiscal 2014 spending bill (HR 2216) that would provide the VA with $147.6 billion, an increase of 10 percent. The Senate Appropriations Committee has proposed providing it with $147.9 billion.

Lawmakers and presidents tend to focus most on the annual fray over spending bills, while nodding toward five-year and 10-year budget cycles. There’s little discussion and few good estimates of what the costs of veterans benefits might be stretching out decades, Bilmes said. Other budget experts agree that this is a short-sighted view that masks the steadily accumulating obligations that will weigh on the VA in coming years.

“The problem is far worse than people think,” said Rep. Jim Cooper, D-Tenn., a budget hawk who teaches part time at Vanderbilt University’s Owen Graduate School of Management.

Several lawmakers are trying to get a better understanding of what the VA’s budget might look like in the years ahead.

The House Veterans’ Affairs Committee is slated to discuss at a July 17 hearing a draft bill from its ranking Democrat, Michael H. Michaud of Maine, that would create a position for a chief strategy officer to aid in long-range planning and to bolster the VA’s analytical and cost-estimation capabilities. Patty Murray, the No. 4 Senate Democrat, held a Veterans’ Affairs Committee hearing in 2011 on the lifetime costs of caring for those harmed in the Iraq and Afghanistan wars. She says she remains concerned about funding these needs.

“It’s not just the number of new veterans that pose a challenge. It’s also the extent of their wounds, both visible and invisible, and the resources it will take to provide them with quality care,” Murray said. “The commitment we have to our veterans is non-negotiable. Not just today, but far into the future.”

There’s also concern that as the U.S. continues to extract troops from the countries, and as the wars recede, today’s fervent support for veterans also will fade.

The costs of caring for Iraq and Afghanistan veterans have not yet hit the federal budget in a big way. There will be decades of disability benefit payments and the costs associated with sophisticated medical treatments needed to address injuries, such as the loss of more than one limb to roadside bombs. A study published in a VA journal found that average lifetime costs for prosthetics needed by an Iraq or Afghanistan veteran who lost multiple limbs might average $2.9 million.

Bilmes has proposed starting a trust fund for veterans that would ensure future service capabilities. Congress could appropriate money for this trust fund while appropriating for armed conflicts, she said. This approach would force lawmakers to consider how much Americans would have to spend in total expenses for wars.

“It would more closely approximate what the costs of war are,” Bilmes said. “We should be setting aside some money and investing it.”

Creating such a trust fund also might help veterans stake their claims to needed federal dollars in the future if support for veterans services weakens as the Iraq and Afghanistan wars slip deeper into the past.

“At this point, it’s hard to now know what the public attitude will be,” she said.