“The traditional argument has always been that Social Security is very popular because it’s not seen like a traditional welfare program,” said Kyle Pomerleau, a resident fellow at the conservative-leaning American Enterprise Institute. “What you pay in roughly corresponds to what you get. Once you start taxing certain levels of income without providing additional benefits based on that tax, you are breaking that link.”

As such, the new Democratic approach to Social Security amounts to a test of what affluent liberals are willing to sacrifice to accomplish progressive goals. For a sign of how ostensibly progressive Democrats can recoil at tax changes that affect their pocketbooks, nearly all Democratic senators recently voted to eliminate a cap on the deductibility of state and local taxes. The deductions favor high-income people in high-tax states, and the cap was part of the Republicans’ 2017 tax overhaul.

Elizabeth Warren, who has the most detailed plan, would tax earnings above $250,000 at a 14.8 percent rate, including both the employees’ and employers’ share. This would finance an extra $200 a month in retirement or disability benefits for beneficiaries of Social Security — a 15 percent increase for the average recipient, devised to help lift many retirees out of poverty. It would also expand Social Security benefits for people like widowed spouses and those who worked as caregivers outside the formal work force.

Bernie Sanders would also apply the current 12.4 percent combined Social Security tax rate to all income above $250,000. Joe Biden has pledged to increase benefits and solidify Social Security’s finances without detailing exactly what changes to payroll taxes he would use to do so.

A bill supported by a broad coalition of House Democrats would apply the current tax of 12.4 percent to all earnings above $400,000, and gradually raise the combined rate to 14.8 percent.

Ms. Warren’s proposal hasn’t received as much attention and debate as her proposed wealth tax on families with assets of more than $50 million. But her Social Security plan would affect around seven million Americans, compared with the 75,000 that her advisers estimate would be affected by the wealth tax.

“She will extend the program’s solvency by nearly two decades by asking just the top 2 percent to contribute more,” said Saloni Sharma, a Warren campaign spokeswoman. “She will provide a $200 immediate increase in benefits across the board for every current and future beneficiary — the biggest increase in benefits in nearly 50 years.”