Billionaire businessman Donald Trump suggested this week his nearest rival for the Republican presidential nomination may be ineligible for office and won a daylong echo across the political press, despite Texas Sen. Ted Cruz’s attempt to brush off the commentary.

In raising the issue, Trump said Republicans should be concerned about Democrats hog-tying Cruz with a yearslong legal challenge -- and indeed an effort to do just that already is afoot.

Rep. Alan Grayson of Florida, an attorney and Democratic Senate candidate, tells U.S. News he will file a lawsuit challenging Cruz’s eligibility should he overtake Trump and win the nomination -- a scenario that’s at least plausible with the senator besting Trump in some Iowa polls.

Cruz was born in Calgary, Canada, in 1970 to an American mother and a Cuban father who later gained U.S. citizenship. There’s no court precedent on whether foreign-born Americans meet the Constitution’s “natural-born citizen” requirement, but there’s more to scrutiny of Cruz’s eligibility.

“If he’s not qualified to be president according to our Constitution, then he certainly should not serve,” Grayson says, poring over his notes for the possible lawsuit. “There’s quite a lot of stuff here.”

In addition to the question of whether Cruz’s birth in Canada disqualifies him from being considered a natural-born citizen, for which there are clashing historical claims, Grayson notes there’s disagreement about whether both parents of U.S. citizens born overseas must be citizens.

And then there’s Cruz’s mother, Eleanor Cruz.

Grayson says Cruz may have forfeited her U.S. citizenship by taking a Canadian oath of citizenship, and that he’s seen no evidence she actually was born in the U.S.

Cruz’s mother “may have elected to give up her U.S. citizenship -- she wasn’t there on a visitor’s visa for five years, that’s for sure,” he says.

Grayson says “if his mother, who clearly worked in Canada for years and years, did so while becoming a Canadian citizen and taking an oath, which is how you do it in Canada, she lost her citizenship by U.S. law, specifically Section 349 of the Immigration and Nationality Act.”

Section 349 says Americans can lose their citizenship if they take loyalty oaths to foreign governments.

“There’s a counter-argument, there are some court cases that have watered down Section 349,” Grayson concedes. “It’s up to some court to decide whether Section 349 means what it say or not or whether it applied to her circumstances. We need more information at this point.”

“Another open question,” he says, “is why is there no record of her birth in the U.S.? Both the senator and others say she was born in Delaware, but there’s no record of it.”

Grayson declined to say if his staff is actively investigating the matter, and says it doesn’t matter to him whether his position wins him support or condemnation. The self-styled “congressman with guts,” however, bristles at the suggestion that his views are similar to those of the “birther” movement that questions President Barack Obama’s eligibility on the unproven theory he was born abroad.

“The Obama birthers are loons,” Grayson says. “There’s no plausible legal argument that Obama is not qualified to be president, that’s ridiculous. There’s a very good legal argument that Ted Cruz is not qualified to be president.”

Rick Tyler, a spokesman for Cruz's presidential campaign, says Grayson’s inquiry into Eleanor Cruz’s citizenship status is “patent nonsense.” He says he’s seen a copy of her U.S. birth certificate and that she did not become a Canadian citizen.

“Eleanor Cruz, like Ted Cruz, has never breathed a single breath of her life not being a U.S. citizen,” Tyler says. Mrs. Cruz lives a floor above the senator’s family in Houston and volunteers regularly at campaign headquarters.

Tyler says it’s unlikely, however, that the campaign will be forced to verify in court information about Eleanor Cruz’s legal status or address the more common arguments about eligibility. “There won’t be a lawsuit because [Grayson] won’t have any standing to file one,” he predicts.

Cruz’s campaign is attempting to shrug off the issue, as it did last year by pointing to a Harvard Law Review article from two past solicitors general that proclaimed Cruz a natural-born citizen, writing a 1790 law included in that term the children of U.S. citizens overseas (Grayson and others interpret that law as requiring both parents be citizens).

Cruz told reporters in Iowa on Wednesday that “as a legal matter it’s quite straightforward" and “settled law,” appearing -- or attempting to appear -- unconcerned.

But some prominent members of the birther movement say it's not settled law. They note past candidacies are different and were not litigated, including the 1968 GOP presidential candidacy of Michigan Gov. George Romney, who was born in Mexico. Arizona Sen. John McCain, the GOP nominee in 2008, they note, was born in the Panama Canal Zone when it was a U.S. territory.

“I really like Cruz and believe he is a patriot, but he is ineligible,” says legal activist Larry Klayman, who in 2014 asked the Department of Homeland Security to begin deportation proceedings against Obama.

But Klayman believes courts would not take a challenge to Cruz’s status.

That’s also the feeling of Soviet-born dentist-turned-lawyer Orly Taitz, who filed several lawsuits arguing Obama was ineligible to be president. She says she believes Cruz is not a natural-born citizen, but says she may not pursue the matter in court after repeated Obama-related defeats.

Taitz says she also believes Florida Sen. Marco Rubio, another Republican candidate for president, is not a natural born citizen because his parents were recent arrivals from Cuba.

“Let’s say we have a Cuban missile crisis a few years from now. What allegiance will they show?” she says, warning a hands-off approach from courts means that hypothetically “anybody could run for president -- it could be the son of Ayatollah Khomeini, it could be the son of the king of Saudi Arabia, it could be the son of Mullah Omar or the son of [Islamic State group leader] al-Baghdadi.”

Maricopa County, Arizona, Sheriff Joe Arpaio, who convened a “cold case posse” to probe Obama’s birthplace and then declared the president’s birth certificate a “computer-generated forgery” in 2012, after it was released at the instigation of Trump, says he’s not sure if Cruz is a natural-born citizen.

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“Cruz, I don’t see any fraudulent document. I mean, he’s an open book with his records so why would I be interested in him?” Arpaio says. “I don’t care where he came from. I don’t care where Obama came from. I just care about a fake document, a birth certificate, that’s it.”

The sheriff, who is controversial for his hard-line stance against illegal immigration and his colorful treatment of prisoners -- forcing them to wear pink underwear and serving them “bread and water” for defacing American flags -- says questions about Obama’s birth certificate are not done.

“It’s not over with yet,” Arpaio says. “I need a couple lucky breaks and we’ll go public again.”