Washington (CNN) President Donald Trump's legally dubious promises to end birthright citizenship have reignited debate in Congress, with some Republicans taking the opportunity to push legislation aimed at the long-standing guarantee of citizenship, though the chance of any proposal advancing beyond a talking point on Capitol Hill remains slim.

Under the historical interpretation of the 14th Amendment of the Constitution, anyone born in the United States is a citizen, with limited exceptions. Children of undocumented immigrants in the country have long been granted citizenship under that interpretation, but the President and some Republicans on Capitol Hill want to end that.

On Wednesday, Trump tweeted that birthright citizenship "will be ended one way or the other." Later in the day, he repeated his claim that he can eliminate birthright citizenship via executive order, although he said his preference would be for Congress to pass legislation.

"I believe you can have a simple vote in Congress," Trump told reporters as he left the White House.

Then he said at a rally in Fort Myers, Florida, on Wednesday night that birthright citizenship has "created an entire industry of birth tourism, big business, where pregnant mothers travel to America to make their children instant American citizens." He called birthright citizenship a "crazy policy" that costs "billions of dollars a year," though he provided no proof for his claims.

Republican Sen. Lindsey Graham of South Carolina, a critic-turned-ally of the President, said on Tuesday that he plans to introduce legislation in line with Trump's vow of executive action, while Republican Rep. Steve King of Iowa, an immigration hardliner who has been rebuked by members of his own party for incendiary comments on immigration and diversity, seized on the President's remarks to promote legislation he has previously introduced to end birthright citizenship as it currently exists.

It's not likely that any legislation challenging birthright citizenship would pass out of Congress, in part because there's no broad base of support on Capitol Hill in favor of doing so and any effort to challenge the policy would be highly divisive.

"At this point, it's really a minority within the Republican Party that's advocating for the end of birthright citizenship," said Sarah Pierce, a policy analyst at the nonpartisan Migration Policy Institute. "There have been bills that have been introduced since the early 1990s that would limit or end birthright citizenship, but they have never had enough support to pass even out of committee, much less out of Congress."

Legal experts have thrown cold water on Trump's assertion that he could end birthright citizenship via executive order, by arguing that it would take the successful passage of a constitutional amendment to do so -- a very high hurdle to clear, since that would necessitate a two-thirds majority vote in both the House and the Senate and ratification by three-fourths of the states.

Legislation like what King has introduced does not attempt to alter the text of the Constitution as it is written, but rather seeks to reinterpret the way a key passage of the 14th Amendment is commonly understood. The bill would restrict birthright citizenship so that children born in the United States to unauthorized immigrants would not automatically be granted citizenship. It currently has 48 cosponsors, all of whom are House Republicans.

Many legal experts believe, however, that efforts to reinterpret the 14th Amendment would not pass constitutional muster.

"The bill Rep. King is proposing would be unconstitutional under the Supreme Court's long-standing interpretation of the 14th Amendment," said Stephen Vladeck, CNN's Supreme Court analyst and a law professor at the University of Texas School of Law. "The only way the bill could be upheld is if the Supreme Court reverses itself or if the Constitution is amended."

Graham has not yet spelled out the specifics of the legislation he has said he will introduce, though he has indicated in the past that he would support a constitutional amendment.

On Tuesday, Graham tweeted that he plans "to introduce legislation along the same lines as the proposed executive order" from the President. Later on Tuesday, Graham tweeted , "I will be introducing legislation to deal with the issue of birthright citizenship for children of illegal immigrants -- in a prospective manner -- as I have always contended it has become a magnet for illegal immigration in modern times."

The senator's office declined to provide any further details about the legislation. CNN has reached out to King's office for comment and has yet to receive a response.

Regardless of whether it would withstand legal scrutiny, legislation challenging birthright citizenship is more of a political messaging tool for now than a serious prospect for passage. However, it is always possible that the President's push to highlight the issue could end up changing the political dynamic on Capitol Hill.

"The President's stand could create political cover for more people to come out in favor of ending birthright citizenship and we have seen some fringe ideas on immigration come into the mainstream under this presidency," Pierce said. "That said, it would be highly unlikely that any of these proposals would advance in Congress."

In an apparent effort to suggest that efforts to end birthright citizenship have bipartisan support, Trump took to Twitter on Wednesday to point out that former Senate Democratic leader Harry Reid once railed against birthright citizenship, back in 1993 as a senator from Nevada. Reid later disavowed that position, however.

The now-retired senator responded to the President on Wednesday by saying, "I made a mistake" and that the President is "profoundly wrong."

"This president wants to destroy not build, to stoke hatred instead of unify. He can tweet whatever he wants while he sits around watching TV, but he is profoundly wrong," Reid said in a statement.