For years, Europe's senior managers were awash in pay envy as their American counterparts reaped huge paydays. Soon European chief executives were demanding – and receiving – equally outsized paychecks.

Now the momentum appears to have reversed course, and a backlash is in full swing. There is a movement to restrain executive pay across the pond that appears to be coming, and coming fast, to the U.S.

The shift was spurred by Thomas Minder, the CEO of a family-owned small business in Switzerland, who also serves as a member of national Parliament. The Swiss public has already approved one set of sweeping pay changes and is set to vote on another later this year.

They include binding shareholder say-on-pay votes that directors and managers are obligated to adopt. In the U.S., nonbinding say-on-pay votes were mandated by the Dodd-Frank Act and adopted by the Securities and Exchange Commission in 2011. Now the European Union, as well as the Germans and French, are looking at reforming their own rules to rein in pay.

U.S. efforts to restrain the pay of corporate bosses have gained momentum from a surprising source: the Republican Party. The GOP appears to have recognized that "Main Street" concerns about executive pay have been a successful plank in the Democratic Party's platform over the past few election cycles. A Republican National Committee report released in March recommended that the party take a more populist stance on executive pay.

"We should speak out when a company liquidates itself and its executives receive bonuses but rank-and-file workers are left unemployed," party bosses wrote in the Growth & Opportunity Project. "We should speak out when CEOs receive tens of millions of dollars in retirement packages but middle-class workers have not had a meaningful raise in years."

Another cause of growing boardroom angst is pressure to disclose the ratio of CEO pay to that earned by the rest of the workforce. Dodd-Frank mandated back in 2010 that publicly listed corporations disclose such numbers, but the SEC has not yet adopted the rules that will govern them.

It might not be long before U.S. companies come to regard mere disclosure as small potatoes. The Swiss are considering imposing a hard cap­ on CEO pay that would limit it to no more than 12 times what the lowest-paid employee receives.

Professors Charles Elson and Craig Ferrere of the University of Delaware last year published a study entitled “Executive Superstars, Peer Groups and Over-Compensation – Cause, Effect and Solution.” They concluded that CEO pay has become untethered from both the broader organizational wage structure and from economic fundamentals. The culprit is the widespread use of peer benchmarking. For nearly two decades, compensation committees have routinely set CEO pay in the top quartile of that for their peers. This practice inadvertently created a slippery upward slope.

On, we have long noted that most CEOs' skills are not transferable to other companies, which raises questions about the validity of “peer” groups. We've also been warning compensation committees that they could end up in court for relying heavily on peer benchmarking after so many fingers have pointed to it as one of the causes of skyrocketing CEO pay. Instead, directors should be using alternative benchmarking techniques, like internal pay equity, as well.

Bottom line, peer group surveys are no longer a reasonable way for boards to set CEO pay. The question is whether directors and their advisors will finally wake up to that fact.

If they don't, the lawsuits will follow. Or even worse, mandatory caps on pay, a la the Swiss.

Broc Romanek is Editor of The views expressed are his own.