There's a very simple solution to keeping Social Security solvent. You raise the cap. People who earn more than $110,100 actually contribute a lower proportion of their income to the payroll tax.
Former Labor Secretary Robert Reich explains:
"Back in 1983, the ceiling was set so the Social Security payroll tax would hit 90 percent of all wages covered by Social Security. That 90 percent figure was built into the Greenspan Commission's fixes. The Commission assumed that, as the ceiling rose with inflation, the Social Security payroll tax would continue to hit 90 percent of total income. Today, though, the Social Security payroll tax hits only about 84 percent of total income. It went from 90 percent to 84 percent because a larger and larger portion of total income has gone to the top. In 1983, the richest 1 percent of Americans got 11.6 percent of total income. Today the top 1 percent takes in more than 20 percent. If we want to go back to 90 percent, the ceiling on income subject to the Social Security tax would need to be raised to $180,000. Presto. Social Security's long-term (beyond 26 years from now) problem would be solved."
Alas, the Republican Party wants to privatize Social Security, or just nuke it (mostly the former), so there isn't the political will to do this. But the ceiling was set during the Reagan administration. So if we only followed his approach, there would be no problem.