The report, to be released Friday, documents the changes in the legal and political realms concerning same-sex unions, The Wall Street Journal reported Thursday.
Third Way is a centrist public policy think tank.
The report found a significant movement toward some recognition of gay relationships since 1996, when the federal Defense of Marriage Act was signed into law, the Journal said. That year, 5 percent of U.S. residents lived in cities or state jurisdictions that recognize same-sex marriage; now it's 48 percent.
"The ground has shifted substantially under our feet, and the country is now approaching a tipping point for the first time in history," the report said.
This year may be the year when voters approve same-sex marriage for the first time, Third Way said. Minnesota, Maine, Maryland and Washington state all have gay marriage-related issues on the ballot this fall.
So far, voters in 32 states have defeated marriage rights ballot questions.