The Hill’s Scott Wong filmed the exchange after the vote on Friday.
Ms Dingell, a Democrat from Michigan, chided Ms Greene for not abiding by the Christian concept of respecting neighbours.
“You try being a Christian and start treating your colleagues decently,” Ms Dingell said.
Later Ms Dingell simply tweeted “Hold my pearls” in reaction to the exchange.
The confrontation came after the House passed the Women’s Health Protection Act almost exclusively on party lines, with 218 people voting for it and 211, with Rep Henry Cuellar of Texas being the only Democrat to vote against it.
The bill would codify the protections for abortion as laid out in Roe v Wade. Democrats passed the legislation in response to a law in Texas going into effect that would restrict abortion as soon as cardiac activity is detected, which is typically six weeks into a pregnancy and before most people know they are pregnant.
Texas’s law would also allow people anywhere in the country to sue anyone who “aids and abets” someone seeking an abortion.
Rep Judy Chu of California was the main sponsor of the legislation and had been pushing similar legislation since 2013. But while Democrats have both the House and the Senate and President Joe Biden has criticised the Texas law as “almost un-American,” the bill likely faces opposition in the Senate.
While Democrats have a majority with 50 votes, with Vice President Kamala Harris as a tiebreaker, the bill could die if Republicans filibuster the legislation. Conservative Democrats like Sens Joe Manchin of West Virginia and Kyrsten Sinema of Arizona oppose removing the filibuster, as does Mr Biden.
Ms Chu told the Senate has an active working operation.
“They’re talking to all the Senators that are voting for the bill,” she said, noting there are 48 co-sponsors, with the only Democrats not co-sponsoring it being Mr Manchin and Sen Bob Casey of Pennsylvania. Ms Chu said Senate Majority Leader Chuck Schumer is interested in holding the vote.
“The filibuster, of course, is the obstacle,” she said. “I do think there is a possibility of having a majority in support of this.”
Rather, Ms Chu said the most important thing was making sure that House Democrats support the legislation, a sentiment Rep Hakeem Jeffries, who is chairman of the House Democratic Caucus, echoed.
“The House is the House, the Senate is the Senate and the first step in the process is to make sure the House is on record making it clear that we are going to respect and protect a woman’s right to make a choice about her own health care,” Mr Jeffries said,
But Texas Republicans objected to passing the abortion legislation. Rep Dan Crenshaw, who represents Houston, decried Democrats as “extremists.” Rep Louie Gohmert defended Texas’s law.
“They’ve never seen something a state’s done they didn’t want to take over,” he said. “It’s compassionate, it’s gonna save a lot of lives.”
Rep Kevin Brady repeated Mr Crenshaw’s sentiment saying the Democrats’ agenda is extreme and said it violated previous bipartisan opposition to taxpayer funding of abortion, since the legislation repeals the Hyde amendment, which bands public money being spent on it, which includes programmes like Medicaid.
“That law is saving now 150 babies a day, mainly pre-born of colour,” he said.
But Rep Sheila Jackson Lee, a Democrat from Texas, derided the legislation passed in her state.
“I think this is lifesaving,” she said about Democrats’ legislation, noting that the Texas law will “kill women.”
“We have to save women.”
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