Jessica Riedl, a fellow at the Urban-Brookings Tax Policy Center, said payroll tax increases to shore up Social Security are "extraordinarily unlikely" in the next couple of years, with the program's retirement trust fund projected to run out in 2032.

Riedl told CNBC on Sunday that if such tax hikes happen, they would likely come closer to 2032, the year the program's trustees project the retirement trust fund will be depleted. She said there is no interest on either side in tax increases in the short term.

Riedl on Payroll Taxes Ahead of the Midterms

The retirement trust fund helps pay benefits to eligible workers and qualifying family members, according to the report. The program's trustees said in a June report that it will run out in the fourth quarter of 2032, when retirement benefits would be cut by 22%.

Heading into the midterms, some Democratic congressional candidates have said they would raise or eliminate the payroll tax cap so high earners pay more into the program, the report said.

Akabas and Adcock on Delay and the Midterms

Other experts focused on what delay would mean. Shai Akabas, vice president of economic policy at the Bipartisan Policy Center, told CNBC that 2032 is when beneficiaries will feel the consequences of inaction. "Nothing gets Congress to move like that type of deadline," he said. He added that delay would increase the shortfall.

Dan Adcock, director of government relations and policy at the National Committee to Preserve Social Security and Medicare, told CNBC the group is educating voters that senators elected this year will be among those to deal with the program. Voters "need to be asking candidates" about their plans, he said.

Moreno, Cole and Cassidy on Proposed Fixes

Lawmakers have already floated changes. Sen. Bernie Moreno (R-Ohio) has joined Sen. Elizabeth Warren (D-Mass.) in proposing to raise the payroll tax cap, while Rep. Tom Cole (R-Okla.), chairman of the House Appropriations Committee, has said he is willing to consider raising the tax rate.

Sen. Bill Cassidy (R-La.) had also proposed a $1.5 trillion "pension investment fund," separate from the Social Security Trust Fund, to be funded over five years. In an X post at the time, Cassidy said Social Security "faces a 28.5% benefit cut in just six years if Congress doesn't act."