What's the right retirement age? (Tracy A. Woodward--The Washington Post)

American voters and some politicians occasionally complain that they don't see a real difference between the two political parties. "It seems to me that both parties and the entire political system are to blame," Sen. Rand Paul (R-Ky.) said in announcing his presidential campaign earlier this year, calling on Republicans to choose a candidate with genuinely conservative views. "If we nominate a candidate who is simply Democrat Lite, what is the point? Why bother?" he asked.

When it comes to Social Security, though, the presidential contenders disagree sharply, giving voters the chance to make an important choice about how elderly Americans will live now and in the future.

Jeb Bush, the former governor of Florida, said on CBS's "Face the Nation" Sunday that he thinks the retirement age should be raised.

"We need to look over the horizon and begin to phase in, over an extended period of time, going from 65 to 68 or 70, and that, by itself, will help sustain the retirement system for anybody under the age of 40," he said.

Bush had previously said he favored a higher retirement age, but hadn't offered much in the way of specifics. In his brief comments, he also didn't provide details, so it is hard to be sure what his suggestions would actually mean for retirees in the future.

The challenge is that over the long term, Social Security will  owe more to retirees than the program receives in taxes or has saved up in its trust fund. Raising the retirement age is, in principle, a way of placing the burden of making up that deficit on today's and tomorrow's workers. The thinking is that they'll live longer than their parents, so they should contribute more to the Social Security over time by working a few extra years.

But there's a big asterisk here.

As it turns out, proposals to raise the Social Security age often have the potential of hurting the poor. Wealthier people tend to live longer. As a result, they draw benefits for more years after they stop working until their deaths. Increasing the retirement age by the same amount for everybody could actually result in poorer retirees receiving benefits for a shorter period of time.

The details matter, though. As Andrew Biggs of the conservative American Enterprise Institute has argued, raising the retirement age might result in more Americans applying for disability benefits, because there will be several more years in which they might be injured or fall sick before they reach retirement age. Those disability benefits might make up some of the gap between rich and poor in welfare for elderly workers.

And as Vox's Matthew Yglesias notes, most workers begin drawing benefits early, at 62. The full retirement age is 66 and increasing to 67 for people currently in the work force (not 65, as Bush said). If they take their checks earlier, workers have to give up some of their benefits, but the trade may be worth it for people with demanding, unpleasant jobs that don't pay well. Bush didn't say anything about raising the age at which Americans are eligible to draw from Social Security if they elect to do so before the retirement age.

In his own proposal, New Jersey Gov. Chris Christie -- also a likely presidential candidate -- was more specific, calling for an early retirement age of 64 rather than 62.

[Read more: Christie’s proposed Social Security changes are a political risk.]

Broadly speaking, though, the proposals from the Republican side of the aisle are very different from those advanced by Democrats. Hillary Rodham Clinton, the presidential candidate and former secretary of state, said in April that politicians shouldn't "mess with" Social Security.

"It is not a luxury. It is a necessity for the majority of people who draw from Social Security," she said on the campaign trail in Keene, N.H.

"I think there will be some big political arguments about Social Security," she said.

Given how little common ground there is between the parties on the issue, she might be right.

In the past, party leaders have tried to work out compromises around more moderate changes to the program. President Bush proposed allowing younger workers to invest some of their Social Security payments in stocks and bonds, where the money would ideally generate a larger return over the long run. The proposal faced widespread opposition.

President Obama has offered to expand retirees' benefits more slowly using a less generous measure of inflation, in a way that protects the poorest seniors. Capitol Hill Republicans have been receptive to the idea.

Mike Huckabee, the former governor of Arkansas, is one GOP presidential candidate who has suggested he would oppose changes to Social Security. On the other hand, many Democrats have gone even farther than Clinton, arguing that Social Security should be expanded.

Two of her rivals for the Democratic nomination, former Maryland governor Martin O'Malley and Sen. Bernie Sanders (I-Vt.), have called for more generous retirement benefits.

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

Clinton hasn't yet said what she thinks about that idea, or how she'd suggest altering the program to guarantee that benefits are available for retirees in the future. It's one among several hard questions that will reveal just what kind of Democrat she really is.