AMES, Iowa—Joe Sanberg thinks there just might be a long-shot presidential campaign for him if he can roll his unique attributes together: growing up poor, succeeding in business, making millions on Wall Street, embracing progressive values, and celebrating his Jewish heritage. Medicare for all, the Green New Deal, increasing corporate regulation, and investing in food stamps and Medicaid to help the poor are the kinds of issues that chased Mike Bloomberg out of the race and Howard Schultz out of the party. Sanberg’s twist: He thinks the policies coming out of his party’s left are actually the best ways to...