Govs. Nikki Haley of South Carolina and Chris Christie of New Jersey had harsh words for the White House's handling of the border crisis during a Republican governors' panel at the Aspen Ideas Festival Thursday night.

Haley worried about the potential costs of temporarily sheltering migrant children in states across the country, despite assurances that the federal government would foot the bill.

"We do care about these children … but we also have our own children to take care of," Haley said.

Christie questioned the system in place that allows children to be released into the custody of "possibly illegal" relatives ahead of their court dates. "It's completely illogical and it's why folks get so frustrated with the government," he said.

Of the panel's participants, Haley, Govs. Sam Brownback of Kansas, Scott Walker of Wisconsin, and Rick Scott of Florida all face reelection in November.

Yet the evening's two only electoral comments came from Christie. The first, regarding social welfare and the economy, bashed Mitt Romney's infamous 47 percent comment.

"One of the biggest mistakes of the 47 percent comment was … the vast majority of people don't want to be on public assistance," Christie said. "That wasn't the American dream, at least when I grew up."

Christie later refuted an audience member's assertion that the GOP needs to reevaluate its social platform to attract female and minority voters in the future.

"We're getting pounded because of the way we present ourselves," said Christie, who pointed to his success in New Jersey despite being pro-life. "People want folks who are authentic … but are also tolerant and willing to listen."

Democratic governors will take part in their own Aspen Institute panel on August 2 .