Gerald Welty sits the House Chamber at the Texas Capitol as he waits to hear debate on voter legislation in Austin, Texas, Thursday, May 6, 2021.

As Republicans march ahead with their campaign to tighten voting laws in political battlegrounds, some in their party are worried the restrictions will backfire by making it harder for GOP voters to cast ballots.

The restrictions backed by Republicans in Georgia, Florida, Iowa, Texas and Arizona often take aim at mail voting, a method embraced by voters from both parties but particularly popular with older voters. The new rules, concerned Republicans note, may be billed as adding security or trust in elections but could add hurdles for key parts of the GOP coalition.

On Thursday, Florida Gov. Ron DeSantis signed a wide-ranging voting bill, making his state the latest to tighten its election rules, while lawmakers in GOP-controlled Texas debated new limits on voting well into the night. The push for new restrictions comes even though former President Donald Trump won both states last year and Republican officials touted their elections as fair and efficient. Critics charge the effort is meant to make it harder for Democrats to vote.

The Texas proposals add restrictions on early voting and prohibit county officials from sending ballot request forms to all registered voters. Until last year, it was Republicans who were more likely to cast mail ballots than Democrats were. In 2016, 40% of mail ballots were cast by people who had voted in a GOP primary, compared to 27% cast by Democratic primary voters.

In Arizona, thousands of GOP voters could find themselves no longer automatically receiving ballots in the mail under a proposal that would remove infrequent voters from a permanent voting list.

Florida’s new law requires voters to request their mail ballots every two years, rather than every four. Critics of the idea argue that could lower voter turnout in off-year elections, when already far fewer voters cast ballots.

Any changes to mail voting in Florida is certain to affect older voters. “Anything that makes it harder for people to cast their vote will have an oversized impact on seniors,” said Florida state Sen. Jeff Brandes, a Republican who voted against the bill.

Rep. Chris Turner, D-Arlington, right, and Rep. Rafael Anchia, D-Dallas, left, line up to speak against HB 6, an election bill, in the House Chamber at the Texas Capitol in Austin, Texas, Thursday, May 6, 2021. (AP Photo/Eric Gay)

People gather outside the House Chamber at the Capitol in Austin on Thursday May 6, 2021, to protest House Bill 6, a bill that would create new election-related crimes, boost penalties for existing crimes and raise the profile of partisan poll watchers. (Jay Janner /Austin American-Statesman via AP)

FILE - In this Jan. 12, 2021 file photo, Iowa Gov. Kim Reynolds delivers her Condition of the State address before a joint session of the Iowa Legislature at the Statehouse in Des Moines, Iowa. As Republicans march ahead with their campaign to tighten voting laws in political battlegrounds, some in their party are worried the restrictions will backfire by making it harder for GOP voters to cast ballots. The restrictions backed by Republicans in Iowa, Georgia, Florida, Texas and Arizona often take aim at mail voting, a method embraced by voters from both parties but particularly popular with older voters. (AP Photo/Charlie Neibergall, File)

FILE - In this Nov. 6, 2018, file photo, then Maricopa County Recorder Adrian Fontes speaks at the Tabulation and Election Center in Phoenix. Republicans in several key states are imposing voting restrictions this year that Democrats say will disproportionally affect their voters. “When you restrict access by reducing opportunities for voters, you are suppressing the vote for all voters,” said Fontes. “Many of the restrictions being proposed by Republicans are effectively a product of their ignorance of the voting habits of their own constituents.” (AP Photo/Matt York, File)

Rep. Rafael Anchia, D-Dallas, speaks against HB 6, an election bill, in the House Chamber at the Texas Capitol in Austin, Texas, Thursday, May 6, 2021. (AP Photo/Eric Gay)