On the same day her sweeping Green New Deal proposal went down in the Senate -- with virtually all Democrats voting "present" -- New York Democrat Rep. Alexandria Ocasio-Cortez said she'd be "happy" to accept a Republican congressman's offer to "go underground" and tour a Kentucky coal mine.

Ocasio-Cortez's comments came just days after she admitted in an interview with The New York Post that she was taking only "baby steps" to be more available to her own constituents in person, and urged interested parties to follow her on Twitter in the meantime.

During a House Committee on Financial Services meeting Tuesday in Washington, GOP Rep. Andy Barr suggested Ocasio-Cortez come to his state and meet some coal miners face-to-face and learn how the Green New Deal would affect them. Ocasio-Cortez responded that she'd "be happy" to oblige, according to multiple accounts of the episode.

Barr says his office sent a formal email invitation to Ocasio-Cortez's chief of staff Wednesday.

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Barr has championed the coal industry, while Ocasio-Cortez's signature Green New Deal calls for virtual elimination by 2030 of greenhouse gas emissions responsible for global warming. Republicans have railed against the proposal, saying it would devastate the economy and trigger massive tax increases.

Staggering cost estimates have said the proposal would cost up to $93 trillion -- more than the U.S. govenrment has spent on any program in its history.

The Green New Deal's botched rollout in February included the release of an official document by Ocasio-Cortez's office that promised economic security even for those "unwilling to work," as well as the elimination of "farting cows" and air travel.

No senator voted to begin debate on the legislation on Tuesday, while 57 lawmakers voted against breaking the filibuster. Democratic Sens. Doug Jones of Alabama, Joe Manchin of West Virginia and Kyrsten Sinema of Arizona joined 53 Republicans in voting "no." Sen. Angus King, I-Maine, who caucuses with the Democrats, also voted "no."

The vote had been teed up by Senate Majority Leader Mitch McConnell, R-Ky., in a bid to make Democratic senators -- including several 2020 presidential candidates -- go on the record about the measure. McConnell had called the proposal "a radical, top-down, socialist makeover of the entire U.S. economy."

Sen. Mike Lee, R-Utah, called the Green New Deal "ridiculous" and displayed pictures of dinosaurs, cartoon characters and babies on the Senate floor. He said he was treating the plan "with the seriousness it deserves."

Ocasio-Cortez, who has warned that the world may be destroyed in 12 years because of climate change unlesss immediate action is taken, later said she had instructed senators to vote "present" on her own resolution.

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For its part, the White House has said it doesn't take Ocasio-Cortez, or her reliance on United Nations predictions, particularly seriously. In 1989, the United Nations warned that the world only had 10 years to avert catastrophic climate change. Again in 2006, a NASA scientist and leading global warming researcher declared that the world had only 10 years to avert a climate catastrophe.

Both deadlines have passed.

Fox News' Samuel Chamberlain and The Associated Press contributed to this report.