Likely sanctions against New Hampshire by the Democratic National Committee and a highly competitive Republican primary could incentivize Democratic-leaning independents to participate in the GOP presidential primaries in that state instead of what could be a meaningless Democratic contest.

On Saturday, the Democratic National Committee voted in favor of changes proposed by President Biden to move South Carolina to the front of the primary calendar, displacing New Hampshire, which has held the slot for the past 50 years.

The DNC chairman, Jaime Harrison, said that the new calendar reflects the diversity of America and “puts Black voters at the front of the process in South Carolina.”

“It keeps Nevada, where Latinos have been building power,” Mr. Harrison added. “It adds Michigan, the heartland, where unions built the middle class of this nation. And Georgia, the forefront of the new South.”

The move has created an impasse between the Democratic Party and the state, which has a law on the books mandating that New Hampshire be the first state to hold a presidential primary. Governor Sununu and the Republican legislature say they will enforce the law.

The Democratic National Committee has in turn empowered the chairman to take “appropriate steps” to enforce the party’s calendar changes. That could mean going beyond the existing punishment for a state not following the proper order — losing half their primary delegates.

This could involve a punishment for campaigns that choose to campaign in the New Hampshire primary, though the specifics will be up to Mr. Harrison and, because the calendar hasn’t changed since modern primaries were implemented, it’s not clear what a punishment would entail.

A professor of political science at University of New Hampshire, Dante Scala, said it is “highly unlikely” that the state government will comply with the Democratic calendar, meaning the most likely outcome will be sanctions against the state and potentially the candidates who campaign there.

Because Mr. Biden isn’t likely to see a serious primary challenger if he runs, the decision by the Democrats makes the Republican primary the only consequential election for the 40 percent of state voters who consider themselves independents.

According to Mr. Scala, there are three types of independents in New Hampshire. Some are reliable Republican votes, some are reliable Democratic votes, and some are so-called true independents.

“This might make it even more likely given the mess on the Democratic side,” Mr. Scala said. “The question becomes, would they want to go and influence the Republican outcome?”

A former Democratic congressman of New Hampshire, Paul Hodes, told the Sun that some Democratic-leaning independents might have an interest in “trying to pull the Republican Party back to the center.”

He said that these voters might not choose to do it because of the mess in the primary process, but instead to support Mr. Sununu, who is currently mulling a presidential bid of his own.

“If Sununu runs, we would also expect to see independents voting for him in the Republican primary, doubling down on my first thought,” Mr. Hodes said.

University of New Hampshire polling on the Republican presidential primary shows that Mr. Sununu is the first choice presidential candidate of 4 percent of likely Republican voters.

However, among Democratic-leaning independent voters likely to participate in the GOP primary, Mr. Sununu’s support jumped to 11 percent.

According to the poll, the Republican candidates who would see the biggest increases in their polling numbers due to an influx of Democratic-leaning independents would be the former governor of South Carolina and ambassador to the United Nations, Nikki Haley, and Maryland’s former governor, Larry Hogan.

According to the University of New Hampshire poll, support for Ms. Haley jumps to 32 percent among Democratic-leaning likely GOP primary voters from 8 percent among likely GOP primary voters in general.

Likewise, support for Mr. Hogan rose to 24 percent among Democratic-leaning likely GOP primary voters from 4 percent among likely GOP primary voters in general.

While the calendar changes on the Democratic side could throw a wrench into the Republican Party’s nominating process for 2024, Mr. Scala said that many are looking past the implications that the changes will have for Democrats going forward.

He said that though Mr. Biden is expected to win the nomination without serious competition this cycle, the changes in the calendar, which is now supposed to be re-shuffled every four years, could drastically alter the sorts of candidates who rise to the top of an open field.

“Beyond New Hampshire they’re making significant changes to the calendar,” Mr. Scala said. “We may not know what the ramifications of those changes are until 2028.”