The Heritage Foundation is not offering cash, but it has launched a campaign of its own on Instagram, aimed at getting young people to post pictures of themselves with the sign bearing the hash tag #stopobamacare.
"We want to package the information in a way that the user or the reader is going to be able to digest it," said Ericka Andersen, who heads up the Heritage Foundation's social media effort to reach young adults. "We want to meet those people where they are."
(Read more: Obamacare's key goal threatened by delayed web marketplaces)
The Heritage Foundation is also launching a $500,000 traditional media campaign to continue to press for overturning the Affordable Care Act.
Between the state exchanges, the federally-run marketplaces and political opposition ads, Kantar Media estimates political spending on the rollout of Obamacare could result in $500 million in advertising through 2014.
Insurers and health care providers could spend twice that according to Scott Roskowski, senior vice president of the media firm Television Bureau of Advertising, known as TVB. But they'll likely wait to see how strong enrollment proves, in the face of continued opposition to the law.
"If the sign ups happen in a major way," said Roskowski, "this health-care category, which has traditionally been a $600 million category across all mediums, now could suddenly be a billion dollar category."
The Obama administration is hoping to enroll more than 2.5 million young adults through the state and federal insurance exchanges this fall.
(Read more: Obamacare exchange readiness going down to the wire)
Commonwealth Fund's Collins says to get strong enrollment among young adults, the exchanges and insurers will need to spread awareness about subsides that will bring help bring premium costs down, as well as lower-cost catastrophic plans aimed at those under 30, who earn too much for premium assistance.
The bottom line, according to Collins: "Affordability is going to be key."
—By Bertha Coombs. Follow her on Twitter: @berthacoombs.
(CORRECTION: An earlier version of this story misstated the names of Peter Lee, of Covered California, and Scott Roskowski, of TVB.)