Here are the numbers: In 2007, there were 20.9 Americans 65 and older for every 100 Americans between the ages of 20 and 64 — that is, the people of normal working age who essentially provide the tax base that supports federal spending. The Social Security Administration expects that number to rise to 27.5 by 2020, and 31.7 by 2025. That’s a lot more people relying on federal social insurance programs.

Nor is demography the whole story. Over the long term, health care spending has consistently grown faster than the economy, raising the costs of Medicare and Medicaid as a share of G.D.P. Cost-control measures — the very kind of measures Republicans demonized last year, with their cries of death panels — can help slow the rise, but few experts believe that we can avoid some “excess cost growth” over the next decade.

Between an aging population and rising health costs, then, preserving anything like the programs for seniors we now have will require a significant increase in spending on these programs as a percentage of G.D.P. And unless we offset that rise with drastic cuts in defense spending — which Republicans, needless to say, oppose — this means a substantial rise in overall spending, which we can afford only if taxes rise.

So when people like Mr. Boehner reject out of hand any increase in taxes, they are, in effect, declaring that they won’t preserve programs benefiting older Americans in anything like their current form. It’s just a matter of arithmetic.

Which brings me back to those Republican freshmen. Last year, older voters, who split their vote almost evenly between the parties in 2008, swung overwhelmingly to the G.O.P., as Republicans posed successfully as defenders of Medicare. Now Democrats are pointing out that the G.O.P., far from defending Medicare, is actually trying to dismantle the program. So you can see why those Republican freshmen are nervous.

But the Democrats aren’t engaging in scare tactics, they’re simply telling the truth. Policy details aside, the G.O.P.’s rigid anti-tax position also makes it, necessarily, the enemy of the senior-oriented programs that account for much of federal spending. And that’s something voters ought to know.