Is Lyndon Johnson partially to blame for the rise in single-parent homes?

[Okay, maybe Mike Johnson is a competent parliamentarian.]

No he is not, and even if he were it wouldn't be as bad as OP is making it sound, for the reasons Christian Man lays out. Commodifying interpersonal relationships is what has hollowed out American family systems, not a noble failed attempt at decommodifying them. I'd argue that the harder edges of the sexual revolution were just such a commodification, but the sexual revolution was not a Great Society program.

[Okay, maybe Mike Johnson is a competent parliamentarian.]

Of course he is. The Great Society's welfare programs punished kids and mothers for having men in the home.

Pretty much all family welfare schemes "punish" either being or married or not being married, once one accepts a definition of "punishment" that extends to "not getting, or getting less of, a particular benefit". This is maybe a distant fifth or sixth in a list of cultural and political changes of the 1960s that disincentivized two-parent homes.

[Okay, maybe Mike Johnson is a competent parliamentarian.]

If we're discussing the specifics of AFDC now, it's worth noting that the "man in the house" rule was introduced, at first, out of concern for the sexual morality of single mothers, since the (racist, classist, sexist) assumption was that any unrelated adult male present was tantamount to a revolving door of boyfriends.