Congressional Republicans who support the administration’s free-trade agenda are pleading for President Barack Obama to make the issue a top priority.

But some Republicans and free-trade supporters also cautioning behind the scenes that the president should move carefully.

Make the issue too much about himself, and conservative Republicans could turn against granting the administration fast-track trade negotiating authority lest they be seen as handing Obama a major economic victory.

“He’s in a tough spot, because Republicans don’t want to give him a win. And Democrats are running away from him,” said one lobbyist working on trade issues who would only discuss the political sensitivities on background.

Sen. Orrin G. Hatch of Utah, the top Republican on the Finance Committee, on Tuesday made clear he wants Obama to do more to push for Trade Promotion Authority, as fast-track is formally called.

“No complex, economically significant trade agreement has ever been negotiated by any administration and approved by Congress without Trade Promotion Authority,” Hatch said in a speech at the Center for Strategic and International Studies. “Sadly, this administration’s enthusiasm for TPA seems tepid at best.”

Hatch called for “active engagement” by Obama. “We need total political commitment from this administration to advancing TPA this year. Without it, we simply will not succeed,” Hatch said.

Christopher Wenk, the U.S. Chamber of Commerce’s senior director for international policy, said it’s not clear yet whether more Obama involvement in pushing for the trade agenda might cost GOP votes.

But, he said, it’s worth the risk.

“There is no substitute for presidential leadership on an issue like trade,” Wenk said. “Trade is a challenging issue for Democrats politically. It would be helpful if he was out there talking about this more.”