DENVER — It’s traditional for Americans to threaten to move to France or Canada when their candidate loses, but this year some disappointed voters are implementing a different plan.

In the wake of the Nov. 6 election, petitions seeking to secede from the union have been filed on behalf of 23 states on the White House website, https://petitions.whitehouse.gov/petitions. Most of the petitions contain the same wording and ask to withdraw “peacefully” from the United States in order to form independent governments.

Critics describe the effort as a bit of an overreaction. “Anyone who wants their state to secede from the union is someone whose brain has already seceded from their body,” said John Andrews, director of the conservative Centennial Institute at Colorado Christian University.

Still, the White House may have to take the requests seriously. According to the website, any petition receiving 25,000 online “signatures” on the “We the People” page within 30 days of posting will receive a review by the appropriate executive department and a response from a White House staffer.

As of Monday, the Texas petition had already exceeded the 25,000-signature threshold, and the Louisiana petition was fast approaching the cutoff with more than 18,000 signatures. Most of the petitions were posted online Nov. 10, which means they have until Dec. 10 to qualify for a response.

It’s impossible to tell from the website who is behind the drive, given that those signing the petition only use their first names, last-name initials, and city and state of residence. The website does show that most petitions include the John Hancocks of signers from other states.

Steve Eichler, CEO of TeaParty.org, said his organization isn’t involved with the petition drive, but added that he wouldn’t be surprised if tea party advocates were at the root of it.

“We have not put out anything seceding from the United States, but the feedback we’re getting shows that people believe that their elected state leaders are more in tune with their needs than those of the federal government,” said Mr. Eichler.

He added that support for secession has cropped up in comments on the organization’s blogs. “People are feeling disenfranchised, they’re feeling a loss of voice, and they just don’t know what else to do,” he said.

Many of the petitions make their argument by quoting extensively from the Declaration of Independence, although some also add that the federal government has grown too large.

“The U.S. continues to suffer economic difficulties stemming from the federal government’s neglect to reform domestic and foreign spending,” says the Texas petition, which had more than 34,000 signatures as of Monday evening.

The Oregon petition argues that the federal government is guilty of an “abuse of power” by forcing “unconstitutional laws over [its] own citizens.”

Seth Masket, political science professor at the University of Denver, said the petitions may be a good way to blow off steam, but that they carry no legal weight.

“It’s hard to see this as anything other than sour grapes,” said Mr. Masket in an email. “These petitions have no legal power and no president would ever agree to them. It’s a way to register dissent with the way the majority of the country voted last week, but it’s little beyond that.”

Then again, said Mr. Eichler, the petitions could be the start of something big, such as the first call for a constitutional convention.

“I’m glad people can vent their frustrations, but what if it’s more than that?” he said. “What can we do to stop this encroachment into states’ rights? What are the tools? Well, there aren’t too many of them, but one of them is a constitutional convention.”

Petitions have been filed on behalf of the following states: Alabama, Arizona, Arkansas, Colorado, Florida, Georgia, Indiana, Kentucky, Louisiana, Minnesota, Mississippi, Missouri, Montana, New Jersey, New York, North Carolina, North Dakota, Oklahoma, Oregon, Pennsylvania, South Carolina, Tennessee and Texas.