When President Barack Obama introduced a new retirement savings plan during his State of the Union speech last month, the Republican response was uncharacteristically muted. Although Republicans were upset about the president’s new reliance on executive authority to push his agenda, they had few harsh words about the details of the retirement idea.

Dubbed MyRA, Obama’s initiative is intended to allow workers who do not have access to other workplace savings plans to open an account overseen by the government that would invest in low-risk Treasury bonds. It’s a relatively modest proposal, one that would be entirely voluntary for employers and employees and would only guarantee low returns to minimize risk.

“I certainly will look at that,” said Rep. Phil Roe, R-Tenn., ranking member of the subcommittee on pensions at the House Education and the Workforce Committee. “Anything for economic security downstream, I will look at that.”

“I’m almost for anything that would allow people to save more and take care of the future,” said Sen. Orrin G. Hatch, R-Utah.

The GOP’s reticence is no accident. Even in an era of bitter partisanship, there is agreement among experts on the left and the right that the retirement security of Americans is a pressing issue. What’s more, there’s broad agreement on how to fix the problem.

One key solution, many on both sides agree, would be some form of automatic deduction from worker paychecks into a retirement savings account, with workers given the choice of opting out. The idea was featured prominently in a Heritage Foundation report and in a study by the liberal Center for American Progress.

Behavioral economists have long found that workers are much less likely to voluntarily deduct part of their paychecks to finance a retirement account. In workplaces where the employer automatically enrolls new employees in a plan, the pickup rate increases. One study found enrollment in retirement plans grew from 37.4 percent to 85.9 percent after it became mandatory.

That suggests that automatically signing up workers for a retirement savings plan would go a long way toward winnowing the gap between what Americans have saved and what they will need to cover basic expenses in retirement. According to the Employee Benefit Research Institute, that gap now stands at $4.6 trillion.

Obama has also embraced the idea of mandatory savings and included language in his budget proposals to create automatic individual retirement accounts for people who do not have a work-based retirement plan such as a 401(k). The administration’s idea would mandate that employers with more than 10 employees set up IRAs for their workers. The proposal includes tax credits to soften the blow on smaller firms.

Some in the private sector are also on board with creating new kinds of retirement vehicles, which would bring more business to the financial services industry without necessarily placing more risk on employers.

Ron O’Hanley, former president of Fidelity Asset Management, and Laurence Fink, CEO of the asset management firm BlackRock, have endorsed forms of automatic retirement accounts.

Sen. Tom Harkin, D-Iowa, chairman of the Senate Health, Education, Labor and Pensions Committee, frequently calls retirement security “one of the most under-reported crises facing us as a nation.”

Although there may be consensus on the broad strokes, the details are much more complicated. Partly for that reason, retirement security proposals have gone nowhere in Congress, which has been more focused on current concerns than on threats that may be several years into the future.

For example, any proposal that would increase the administrative burden on employers is likely to run into opposition from small-business owners. According to the National Federal of Independent Businesses, only about 27 percent of small businesses currently offer retirement plans such as a 401(k).

Mandating that they offer some sort of automatic deduction, even if they are not on the hook for a contribution themselves, would create an untenable regulatory burden, said Eric Reller, a spokesman for the NFIB.

“There are so many regulations going into effect every day that it would just be another thing to add to that,” he said.

At the same time, any proposal that mandates employers offer plans such as 401(k)s is unlikely to find much support among Capitol Hill Republicans, according to a Senate aide. But Republicans might support an idea that automatically deducts money from workers’ paychecks to set up some form of retirement account, provided employers were absolved of fiduciary responsibility and employees had the chance to opt out.

“If you’re automatically enrolled and you can opt out, it’s not a mandate,” the aide said. “But you are taking advantage of human nature and behavioral science.”

But states, including California, that have sought to create their own state-run mandatory automatic retirement savings programs have angered industry groups that say they would duplicate existing programs in the private sector and still leave employers vulnerable to lawsuits.

Liberal groups also have not all embraced Obama’s automatic IRA proposal, saying they prefer a system in which assets are pooled to minimize fees and risks. Under the current IRA or 401(k) system, people risk outliving their savings and lose a significant amount of their assets to fees, said David Madland, a retirement policy expert at the Center for American Progress.

“At the theoretical level you can get people to say, ‘Yes, it would be a great idea,’ and then — the old saying that my grandmother used to use — the devil is in the details,” said Dallas Salisbury, president and CEO of EBRI. “You end up with different pieces of it having different levels of consensus. Obviously, if there was a total consensus, it would already have been done.”

In 2011, the Heritage Foundation issued an extensive report called “Saving the American Dream” that outlined a series of policy solutions it said would boost economic security. It called for a nationwide automatic retirement account that would eventually set aside 6 percent of workers’ paychecks unless they opted out.

Two years later, the Center for American Progress called for a new form of retirement account in which contributions from workers would be pooled and professionally managed by a nonprofit entity. Pooling resources would minimize the market risk now borne by individuals in 401(k) plans or by employers in traditional defined benefit plans. The Center for American Progress proposal would also likely result in much lower fees than savers are currently paying.

“Most people realize if you don’t do anything you’re going to have a situation that neither conservatives nor liberals like,” said Madland. “You’ll have a lot of people in poverty or close to it and you’re going to have more people relying on government programs.”

Harkin has also proposed something similar to the Center for American Progress plan. In legislation (S 1979) introduced last month, the retiring senator outlined a plan to automatically deduct and invest 6 percent from paychecks of workers who do not have access to workplace retirement vehicles. The accounts, known as USA Retirement Funds, would be mandatory for employers with more than 10 employees. In Harkin’s idea, assets would be pooled and managed professionally and would provide an annuity upon retirement, guaranteeing retirees a monthly check for the rest of their lives.

On the Republican side, Hatch has introduced legislation (S 1270) that would make it easier for smaller employers to voluntarily set up accounts for workers. Known as “starter 401(k)s,” the accounts would not be subject to the same administrative burdens that employers who offer traditional 401(k) plans must shoulder.

The legislation is intended to entice small businesses and start-ups to offer the starter 401(k) plans by making offering tax credits and by allowing them to forgo having to match their employees’ contributions.