AARP was one of the most powerful voices speaking out in support of the rule, before its issue, and now that the DOL has spoken, the organization is determined to keep the rule in place—despite efforts by Republicans and segments within the financial industry to overturn it.

At the end of April, the House passed a resolution of disapproval of the rule in a vote of 234 to 183, with a single Republican voting against the resolution.

The Senate plans to take up the resolution in the next few weeks. They have until June 7, under the Congressional Review Act, to do so—although should they manage to pass it and send it to the White House, it's bound to die there. The Office of Management and Budget issued a statement at the time the House passed the resolution that said, "If the President were presented with the House disapproval measure, he would veto the bill."

For its part, AARP isn't letting any grass grow under its feet in evaluating how strongly the public is behind the fiduciary rule.

The survey, specifically designed to gauge the public's support for the rule, as well as to get people's reactions to the importance of receiving financial advice that's in their best interest, indicated that 91 percent of retirement account holders agree with the rule.

Among those who have received professional advice in the past, the percentage is even higher, at 93 percent, compared with those who haven't received professional advice, at 87 percent.

Regarding the importance of advice being in the client's best interest, 88 percent of retirement account holders said that was important. And again, the ratio was higher among those who have previously received professional advice: 92 percent say it's important, compared with 79 percent of those who have not received professional advice.