Twitter is not exactly known as a platform for centrist, middle of the road, political discourse.

But Third Way, the prominent think tank for moderate Democrats, is hoping to change that. The group is targeting roughly 10,000 “influencers” on the platform by promoting paid content that aims to change the progressive conversation to centrist chatter ahead of 2020. And they’re doing so, in large part, by encouraging the individuals they’re targeting on Twitter to not pay too much attention to Twitter.

“Checking Twitter might be a quick way to tune into the political conversation, but it’s probably warping your sense of the electorate,” Third Way’s official account tweeted earlier this week, linking to an article in The New York Times.

“Playing to the far left on Twitter is a surefire way to leave moderate & independent voters at home on election day,” a portion of another tweet reads.

For years, Third Way has tried to keep the Democratic Party from lurching too far left. They’ve done so, primarily, by pitching lawmakers on the idea that the path to a sustainable governing majority lies in more centrist-minded policies. But with Democratic lawmakers continuing their leftward drift, the group is rethinking what type of incentive structures matter. The Twitter campaign is a recognition that social media conversations—and the powerful public opinion shapers who participate in them—can be as influential in shaping how lawmakers act as, say, polling data.

“We don’t want to cede the digital conversation to the far left,” said Matt Bennett, the group’s co-founder and senior vice president for public affairs.

“This is not a grassroots-oriented campaign,” he conceded.

Included in the 10,000 individual the group is targeting on Twitter are elected officials, wealthy donors, and pollsters. Third Way also aims to reach political journalists whose daily reporting ritual includes scanning the platform for news. The group makes it a priority to tag and retweet specific reporters and praise articles they believe captures the under-appreciated centrist mood of the country.

“‘If Democrats go too far to the left, geography will punish them,’ warns @emilymbadger in the @UpshotNYT,” read a recent Third Way tweet referencing a New York Times writer.

So far, Third Way has spent more than $50,000 on Twitter ads since last December, according to figures provided to The Daily Beast. They hope to continue at that pace over the next several months. To achieve that, they have enlisted Precision Strategies, a strategic communications firm whose clients also include Pfizer, General Electric, and Facebook, to convince agenda-setters to “avoid falling off the left edge of the political universe,” as Bennett puts it.

He acknowledges the irony in running ads on Twitter with the primary message that the platform is problematic. “For us, it’s a very double-edged sword,” Bennett said. “On the one hand, one of our messages is ‘don’t pay so much attention to Twitter. Twitter isn’t real.’ On the other hand, you have to go where the people are.”

Ultimately, Third Way’s goal is not simply to influence the influencers, but to shape the direction that the Democratic Party takes heading into the 2020 primaries. For that reason, the group is paying particular attention to high-visibility Democrats in Iowa, New Hampshire, Nevada, and South Carolina, the first four states to vote in the Democratic primary. In recent weeks, for example, the group has been promoting the “#killthecaucus” hashtag, even tweeting: “Caucuses are dying. That is good for democracy,” with a link to a memo written by its senior political analyst.

Such messages have not always gone over well. Bennett acknowledged he has already heard from some irritated Iowa Democrats.

“Sure doesn’t feel that way in Iowa,” one influential Democrat in the state told The Daily Beast when presented with the tweet arguing that “caucuses are dying.”

Meanwhile, one Democratic activist in New Hampshire said the group’s “promoted” tweets, which pop up in specific users’ timelines, are generally unappealing.

“I’m open to some degree to some of their arguments,” the Granite State activist said, “but have zero trust in them or their motives, and they’ve made me more suspicious of anyone pushing those arguments.”

In South Carolina, another critical early voting state, Third Way is not just targeting influencers on Twitter, but also hosting a conference in Charleston next month. Some Democrats in the state have already taken note of their online activity. When asked about an uptick in digital presence, one source said it’s apparent, adding, “I’m in one of their promoted tweets.”

The group is also targeting users in New York and Washington, hotbeds of campaign donors and other powerful political entities. And they’ve already caught the ire of some progressives there.

“Third Way’s so called ‘centrist’ solutions are anything but, because they don't actually reflect the center of public opinion,” New York-based progressive strategist Rebecca Katz told The Daily Beast.

Still, Bennett said he doesn’t expect casual Twitter users to pay any attention to what they’re doing online. “With a Twitter ad, unless you’re interested in this tactic, it just sort of flows past,” he said. “We’re not intending to stop people and say, ‘Whoa.’”