Bipartisan cooperation: Imagine that.

Can we find that same strain of political leader today in our dystopian capital? Somewhere in the halls of Congress, can we find people of divergent backgrounds and political philosophies who can work together to pass historic legislation? I think we can, in the personages of Rep. Jeb Hensarling of Texas, the conservative firebrand who heads the House Financial Services Committee, and Sen. Elizabeth Warren of Massachusetts, the outspoken darling of populist progressives—though the two of them may not realize how much ground they share until they read this column.

I have known Warren and Hensarling for years, and I respect and like them both. I recently had tête-à-têtes with each of them that ran on Fortune.com. (My conversation with Warren is here; my conversation with Hensarling is here.) To be sure, they are diametrically opposed in their philosophical approaches to government. She believes in a proactive role for government in helping working families; he thinks the best thing government can do for them is to get out of their way. She wants more regulation of the financial industry; he thinks that pendulum has swung too far. He thinks federal spending is unsustainable; she wants to spend more on education and research. When it comes to labels, even their rhetoric diverges. When speaking of Main Street America, he says “middle income,” while she says “middle class.”

Yet both of these politicians are smart, sincere, and driven by an overriding passion to help the little guy. And in that, I think they reflect a rising populist sentiment on the left and right that average Americans aren’t getting a fair shake—a feeling stoked by inexorably rising income inequality and the bailouts that followed the financial crisis. During our recent conversations, each would always come back to the plight of working families and small businesses. Both decried the uneven nature of the economic recovery and expressed concerns about the system being stacked against the average Jane and Joe.

Hensarling fretted about the cabinetmaker in his hometown who closed his business because of its regulatory burdens. Warren’s eyes lit up when she talked about trying to help owners of small shops and cafés in Boston’s blue-collar neighborhoods who are contending with high licensing fees and a tax code that favors the big guys. I’m not sure which one got angrier when we talked about “too big to fail” and the inherent unfairness of bailouts. As Hensarling said, “There is some rigging going on, and when big government and big business get in that big bed, it’s not good for middle-income America.”

But can this passion for Main Street compel them to action or cooperation? The issue that seemed to tie them most closely together was the need to reform our loophole-ridden corporate tax code. With her characteristic candor, Warren labeled the code “corrosive,” undercutting the idea of a level playing field and doing nothing to create wealth or productivity. Hensarling put corporate tax reform at the top of his priorities, calling for a flatter, fairer, and simpler code, which he believes would ignite economic growth.

To date, the two haven’t worked together on the issue. Neither has yet shown his or her hand by sponsoring a comprehensive proposal (which might make working together on a compromise easier). Still, in conversation, Hensarling and Warren expressed some optimism that corporate tax reform was an area for bipartisan action. Hensarling recalled that in recent budget deficit negotiations involving Congress and the Obama administration, it was the area where Democrats and Republicans came closest to accord. He also told me that there wasn’t a single deduction, exemption, or other loophole that he wouldn’t be willing to trade for lower marginal rates.

And there’s the rub. While Hensarling and other conservatives want to lower rates, Warren and her allies want to keep rates where they are (or even raise them) and close loopholes to pay for social spending. Yet Hensarling left the door open a tad when I talked with him, suggesting that he might support revenue (not rate) increases if the money was used to reform the Social Security and Medicare systems. (In case you aren’t keeping track, the Social Security Trust Fund is projected to fall short of its obligations in 2033. Medicare is in even worse shape: Its fund will fall short in 2030. So if you are near retirement, you are likely to be confronting benefit cuts in your eighties. Don’t worry: Maybe Chipotle (CMG) will hire you.)

Perhaps corporate tax reform is the place where Hensarling and Warren can make their own bit of legislative history. Corporate loopholes cost the government about $180 billion a year; closing them would raise enough revenue to lower marginal rates and still pick up some revenues to help bolster the Social Security and Medicare trust funds. The latter should be popular with not only current retirees but also young people who are confronting the risk of substantial future increases in the payroll tax. What politician wouldn’t like that?

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Of course, there’s little correlation between a position’s popularity and its chance of success. Just ask former House Ways and Means Committee chairman Dave Camp, now retired. His thoughtful proposal for tax reform in the last Congress never made it out of his own committee.

To succeed, such an effort will need the support of corporate America. Will big companies support a fairer, flatter tax code or fight to the death to keep their special tax breaks? Let’s hope corporate leaders are willing to compete on a level tax playing field. It’s in their long-term interest to do so. Populist sentiment is rising in both parties. It can be directed in positive ways or it can fester into something destructive. For, as Hensarling told me, “if we allow corporate welfare to become confused with free enterprise, we will kill off the free enterprise system.”

Sheila Bair is a former chair of the FDIC and the incoming president of Washington College in Maryland.

This story is from the June 1, 2015 issue of Fortune magazine.