The hostages, who spend 444 days in captivity, have tried for 17 years to seek compensation but have been blocked by the State Department because such lawsuits are barred by the Algiers Accord, the agreement that freed them.
Circumstances, said Sen. Johnny Isakson, R-Ga., sponsor of a Senate bill that would provide the former hostages or their heirs with compensation, have "brought back the memories for everybody who lived through that time," The New York Times reported Wednesday.
Of the 52 hostages held inside the embassy from Nov. 4, 1979, until Jan. 20, 1981, 39 are still living.
In 2012, they picked up 69 co-sponsors on a House bill to let them be compensated through fines on companies caught violating trade sanctions with Iran. A substantial bipartisan effort is percolating in the Senate.
The hostages were seeking money deposited by the shah and impounded by the United States after his overthrow. Isakson's bill also would get the money from fines paid by companies caught doing business with Iran, providing $10,000 for each day of captivity to the hostages or their heirs.
Republican and Democratic administrations have argued interference by the courts and Congress would limit the president's ability to conduct foreign policy. But now the State Department isn't openly opposed since the money would be paid from a different source, the Times said.
Sen. Richard Blumenthal, D-Conn., who co-sponsors Isakson's bill, said the State Department "will continue to work with Congress on this issue."
"My first choice would be for Iran to be the ones to pay it directly," Blumenthal told the Times. "This alternative is clearly a second choice, but it's a just one."
Changing the strategy of compensating the hostages and their heirs from fines makes the legislation viable, he said.
"For a whole bunch of reasons, it's now or never," Blumenthal said. "The hostages are aging, and there's a moment of recognition among the American public that we never did right by these people."
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