That's not an accurate statement. Until the the very first "marriage" deduction in the income tax...the 20th century...the federal government had no role in marriage whatsoever. None. Zero.
The states got involved much, much earlier in which they began to codify existing church norms and add property protections for women and children.
The hold up was polygamy, if they did not outlaw it they were told they would not be admitted to the union.
That was long before the 20th century.
They were other places where the fed got involved in marriages, usually in whether a mixed race marriage was "legal".
One these had to do with the Cherokee being forced out of the south. There were mixed marriages and they had to decide who would be forced out and who could remain.