WASHINGTON — Legislation that would outlaw nearly all abortions after the 22nd week of pregnancy was put on a fast track to the House floor on Wednesday after being approved in committee on a party-line vote.

The 20-to-12 vote by the House Judiciary Committee on the Republican-sponsored Pain-Capable Unborn Child Protection Act is the latest instance in which abortion opponents, emboldened by a series of victories in the states, have pursued a new legislative strategy that aims to focus public attention on the disputed theory that fetuses can feel pain.

“Delivered or not, babies are babies, and it has been shown that they can feel pain at least by 20 weeks,” said Representative Robert W. Goodlatte, the Virginia Republican who is the chairman of the committee. “It is time to welcome young children who can feel pain into the human family. And this bill, at last, will do just that.”

A vote by the full House could come as early as next week, aides to Republican House leaders said, though the bill is virtually certain to go no further because of opposition in the Democratic-controlled Senate.