In a Tuesday vice-presidential debate studded with surprising points of agreement between two starkly different candidates, an extended discussion of child care stood out.

Over the past three years, Congressional Republicans, with the help of one key moderate Democrat, essentially killed President Biden’s attempts to create a national affordable child-care system and extend a generous pandemic-era tax credit for families with children.

Nevertheless, on the debate stage, Senator JD Vance of Ohio, Donald J. Trump’s running mate, wholeheartedly agreed with Gov. Tim Walz of Minnesota, the running mate of Vice President Kamala Harris, that shortages of affordable child care are a crisis for American families, and that the federal government should provide cash payments to parents.

“A lot of us care about this issue,” Mr. Vance said. He deftly used the line of questioning to rebut the image of him that has been painted by critics in recent months, as a right-wing scold with dated views on women and motherhood.

“I’m married to a beautiful woman who is an incredible mother to our three beautiful kids, but is also a very, very brilliant corporate litigator,” he said. “A lot of young women would like to go back to work immediately. Some would like to spend a little time home with the kids. Some would like to spend longer at home with the kids. We should have a family care model that makes choice possible.”

In sketching out his beliefs on child care, Mr. Vance sounded more like the moderate Republican he was perceived to be before he became so closely allied with Mr. Trump and the very-online right. He has long been loosely affiliated with a group of conservative intellectuals who have pushed the Republican Party to embrace government spending on child care and cash benefits, in part to encourage parents to have more children as access to abortion has become more limited.