Some business groups and G.O.P. proponents of a paid leave program believe that if it had been broken out and negotiated with Republicans, the way a $1 trillion infrastructure package was at Mr. Biden’s urging, it could have survived, and some think it still could resurrected as a bipartisan initiative.

They said the problem lay with the Democrats’ decision to put paid family leave in the expansive social policy and climate bill — a multitrillion-dollar package financed by large tax increases on businesses and the wealthy — which they knew that Republicans and mainstream business groups would never support.

“In any area that is substantive, when members sit down to actually walk through whether or not we can build good legislation, there are possibilities,” Senator Lisa Murkowski, Republican of Alaska, said. “We’re not being encouraged to work together to solve problems. What we’re being encouraged to do is line up with the team so that we can have the political messaging point.”