Columbia, S.C. (CNN) Some conservatives in South Carolina want to disrupt the state's upcoming Democratic primary and inject chaos into the race for the nomination.

"You know I guess you could call it meddling," said Christopher Sullivan, one of the organizers of the Conservative Defense Fund in South Carolina. "I would love to see the Democrats -- whoever wins the South Carolina Democrat primary -- for everybody else to have accused him of having stolen the election because he was actually elected with Republican support and therefore prolonged the chaos and the disruption."

In South Carolina, Republicans aren't holding their own presidential primary this year. The state's open primary rules allow for eligible voters to cast ballots in the Democratic contest even if they are registered Republicans. That gives GOP voters a chance to play spoiler in the Democratic contest that is shaping up to be a do-or-die moment for former Vice President Joe Biden and his campaign.

Conservatives in the state have been rallying against the open primary system for years. They say in the past, Democratic voters have cast ballots in GOP primaries and skewed the results of state races to elect more moderate Republicans. Stacy Shea, one of the organizers encouraging GOP voters to turn out and upset the Democratic contest, has collected thick stacks of postcards from Republican voters pledging to support registration by party and "stop canceling out my vote."

This year's Democratic primary is an opportunity for conservatives to give Democrats a taste of their own medicine, organizers say.

"We thought, 'Aha! What would happen if we made a grassroots, state-wide effort to cross over and vote for one candidate in the Democratic primary?' Would that cause enough angst among the Democrats, either elected officials or party members, to maybe come to the table and let's talk about closed primaries?" Karen Martin, a Tea Party organizer in Spartanburg, told CNN.

The movement could also elevate a Democratic candidate that Republicans view as weaker against President Donald Trump in the general election -- though organizers say it was not a key factor in their decision.

"It had nothing to do with his ideology, or that we would rather have Bernie against Trump than Biden, we just want to move the numbers so that the conversation is open on the primaries," Martin told CNN with this twist. "Just for the sake of optics, it would be great to be able to contrast the ideology of an avowed socialist versus a capitalist."

The grassroots campaign doesn't have just one leader. Instead, it is a decentralized movement that includes multiple conservative activists upstate. Some, like Sullivan, nicknamed the effort "operation chaos." He says he isn't pushing any individual candidate. Others, like Martin, are pushing for Republican voters to all cast their ballots for Sanders.

The effort comes at a time when Biden is banking on South Carolina to be his life raft in the race for the Democratic presidential nomination.

And Biden's team there has taken note of the effort. South Carolina Sen. Marlon Kimpson, a Biden surrogate, introduced legislation last week that would require anyone who voted in the Democratic primary to vote in the same primary in 2024, post-Trump, when Republicans will be battling it out to pick a new GOP presidential nominee. The bill is intended to discourage Republicans from meddling in the Democratic primary this time around.

"Somebody had to do something. There is a great effort by the officials of the Republican Party that seek to undermine the Democratic primary," Kimpson said of his bill. "Our democracy is built on strong participation in a primary, not interference by the opposition. And so this bill simply highlights that there is an issue with the Republican Party conspiring to vote for the weakest candidate, they've said that publicly and that is Bernie Sanders."

For its part, Sanders' campaign pushed back on the idea that Sanders would be a weak match-up against Trump.

"Recent reports have made it clear that Donald Trump and the Republican establishment have always been afraid to run against Bernie Sanders going back to 2016 and this is more of the same," Jessica Bright, Sanders' South Carolina state director, told CNN in a statement. "The truth is that Sen. Sanders consistently beats Trump in general election match-up polls in battleground states."

The South Carolina Republican Party says it isn't endorsing the grassroots effort, and it maintains it isn't involved in mobilizing Republican voters to turn out to influence the Democratic primary on February 29.

"While there are some groups and Republican activists that may decide to participate in the open Democratic Presidential Preference Primary on February 29, the South Carolina Republican Party has taken no official stand on this matter nor will it encourage our members to do so," Hope Walker, South Carolina GOP executive director, said in a statement.

Still, Martin says no one from the official Republican Party has called and asked her to stop her effort.

"The state party can't take this route, but activists can. So, I don't think they are angry at us or wanting us to stop," Martin said.

The lack of help from the state Republican Party, however, has frustrated some.

"I believe it to be in our long-term best interest to vote in a manner that is going to get our primaries closed. And if this is what it takes to do it -- to vote where we would ordinary not -- then that is what we are going to do," Hal Roach, a Republican from Greenville, said.

Organizers who are relying mostly on social media and news stories to get the word out about their effort say it's not clear how many Republicans will ultimately participate or if there will be enough to influence the process.

They are insistent, however, that it would only take a few thousand votes to sway the contest. In South Carolina, the Democratic Party awards delegates proportionally, so they argue that even if the effort only took hold upstate, it could still boost the number of delegates Sanders wins.

"In South Carolina, when you have contested primaries on both sides, Republican turnout is usually about twice what the Democratic primary turnout is," Sullivan told CNN. "So if only half of Republicans turned out and voted that would be equivalent of half the democratic primary turnout.. Even if it's a smaller number, 10 to 20%, that can have a huge impact."

Patrick Haddon, a Republican state representative and long-time supporter of closed primaries, says he personally won't be voting for Sanders in the Democratic primary and that it's not clear how much of an impact the activist groups will actually have at the end of the day.

"[It's] one thing to say on Facebook, let's get the masses out, but totally different to get those people to turn out," Haddon said. "There has been a lot of Facebook, social media, one-on-one calls. It has been a pretty good effort, but I'm not sure how it's going to turn out. "

Haddon says that regardless of how successful the campaign really is, he doesn't think Trump can lose to any of the Democratic nominees. But he does think it would be "more fun" to see a Sanders vs. Trump ticket in November as opposed to any of the other candidates, and that the effort does have the potential to impact the Democrats in their primary contest.

"If a vast number of people come out and vote for Bernie, it might affect (the primary), so I can see where the Biden camp might be a little upset about that."