Hillary Clinton said she would be open to a Social Security tax increase on a recent trip to New Hampshire. (Melina Mara/The Washington Post)

CLAREMONT, N.H. -- What to do about Social Security is one of the most important questions that Hillary Rodham Clinton has yet to answer as she lays out her economic agenda for primary voters.

Democrats in Congress, along with other contenders for the party's presidential nod, are saying that a costly increase in benefits is necessary, given how few workers are able to save for retirement.

So far, Clinton hasn't embraced the liberal prescription for Social Security, but her views could be changing. At a town hall here Tuesday, she said she'd be open to a Social Security tax increase proposed by Sen. Bernie Sanders (I-Vt.), her radical rival in the primary.

During the 2008 campaign, Clinton had flatly rejected such an increase. Her comments this week could suggest that she has warmed to the idea, or that she is responding to a broader shift to the left among Democrats.

[Read more: Why rich guys want to raise the retirement age]

Clinton was responding to a question from the audience at a community college about the fact that the wealthy and upper middle class don't pay Social Security taxes on anything they earn above a certain amount. That limit is $118,500 this year.

"I can understand why you'd think that was unfair," the former U.S. senator and secretary of state said, before suggesting an increase in the limit. If the cap were raised, anyone pulling down six figures this year would have to pay taxes not only on their first $118,500, but also on any money they made above that amount, up to the new limit.

Clinton then described an approach similar to Sanders's -- raising taxes only on the wealthiest earners to avoid an increase for people who consider themselves upper middle class.

"We do have to look at the cap, and we have to figure out whether we raise it or whether we raise it a little and then jump over and raise it more higher up," Clinton said.

Many liberal experts on Social Security argue for raising the limit on taxable earnings as a way to bring more money into the program, helping to ensure that benefits will be available for future generations of American retirees. Social Security's main trust fund will be exhausted around 2032, the Congressional Budget Office projects, at which point the system would no longer have the money to pay benefits in full.

Proponents also say that raising the cap would restore fairness to the program.

Since the last major Social Security reform in 1983, the gap between the rich and the poor in the economy has grown. As a result, a larger proportion of the money that American workers make in any given year goes to people whose annual compensation is above the limit, reducing the overall fraction of the country's wages that is taxed for Social Security and eroding the program's finances.

Increasing the cap would ensure that wealthy workers pay "their fair share," said Christian Weller, an economist at the University of Massachusetts, Boston.

Just how much that fair share should be is hard to say. Retirees' Social Security benefits are calculated based on how much they've paid into the system, not their total earnings over their careers. While it might seem odd that the wealthy don't pay taxes on their earnings above a certain amount each year, it's important to keep in mind that they also don't receive benefits on those earnings later on.

Weller argued that all the same, the rich ultimately draw more from Social Security in benefits because they tend to live longer. He said that raising the cap would make the program more equitable.

"It really would put Social Security on a more even footing," said Weller, who is affiliated with the liberal Center for American Progress.

Sanders's proposal -- increasing payroll taxes, but only for the wealthiest earners -- resembles the one President Obama laid out as a candidate in 2008. Obama had promised not to raise taxes on anyone earning less than $250,000 a year, many of whom consider themselves in the upper middle class. Subjecting income over $250,000 to the payroll tax would make up about three-quarters of the program's shortfall over the long term, Social Security's actuaries project.

At the time, Clinton opposed the idea. "I'm certainly against one of Senator Obama's ideas, which is to lift the cap on the payroll tax," she said in a Democratic primary debate then.

So far in this campaign, she has not taken a clear position on the question of Social Security's future.

"What do we do to make sure it is there?" she asked on an earlier trip to New Hampshire. "We don’t mess with it."

A spokesman for Clinton's campaign declined to elaborate on her comments.

Sanders would also increase Social Security benefits. Former Maryland governor Martin O'Malley, a third Democratic candidate, has likewise said that benefits should be increased.

[Read more: A simple guide to the real differences between the Democratic candidates.]

Andrew Biggs, a scholar at the conservative American Enterprise Institute, dismissed Democrats' doughnut-hole approach as a political gimmick. Increasing Social Security taxes, but mainly on the very rich and not on the upper middle class, would not raise enough money to preserve the program, he argued.

There are few good options for improving Social Security's finances. An increase in the payroll tax rate would raise money but would place a substantial burden on the working poor. So could raising the retirement age, as New Jersey Gov. Chris Christie and other Republican presidential candidates have proposed as a way to reduce costs.

"The difficulty for somebody who's running for president as a Democrat now, what they’d like to do is fix the system," Biggs said. "They'd like to do it by raising the tax rate on rich people, not poor people. The problem is, basically, you can't do it."

Weller agreed that just increasing the limit on taxable earnings would not be enough to ensure Social Security's longevity, but he argued that isn't a reason not to do it.

"Raising the cap is one step toward sensible Social Security reform," he said.

Ehrenfreund reported from Washington.