Senate Finance Chairman Max Baucus (D-Mont.) will make his case for moving the long-stalled U.S.-Panama free-trade agreement at a Thursday hearing. But in the House, where Democratic leaders face a heavy lift to get the deal passed, Baucus’ arguments and those of other free-traders are not getting much attention.

“Guess what? Nobody has talked to me about Panama,— said Ways and Means Chairman Charlie Rangel (D-N.Y.), who has yet to hold a full committee hearing on any pending trade deals in the 111th Congress. By contrast, Rangel has conducted four hearings on health reform and two on climate change, both top legislative priorities for Democrats.

Rep. Ron Kind (Wis.), a leader of about 20 Democrats who back the Panama deal, said there has yet to be a major lobbying push on the trade agreement. “I’ve heard from some traditional groups that have never supported trade agreements,— he said. “We hear from them from time to time, but no [new groups].—

Even House Rules Chairwoman Louise Slaughter (D-N.Y.), a longtime opponent of trade deals, said she has received few telephone calls from constituents or lobbyists trying to sway her support on the Panama pact.

Still, Baucus seems intent on building support for the deal. And trade bill supporters warn the whole deal could unravel if it isn’t approved by late June, when current Panamanian President Martin Torrijos leaves office. Trade lobbyists believe the new Panamanian administration is less likely to sign off on the agreement, particularly on the labor and tax provisions being sought in the House.

On Thursday, Everett Eissenstat, the assistant U.S. trade representative for Western hemisphere affairs, will testify on the agreement before Baucus’ panel. Eissenstat is a former staffer to then-Finance Chairman Chuck Grassley (R-Iowa) and a holdover from the Bush administration who helped negotiate the Panama agreement.

Business and labor leaders are also set to testify, but concerns about Panamanian tax enforcement — which has generated concern among House Democrats — may not even come up at the Senate hearing.

Baucus calls the Panama deal “the agreement that’s most ready for action. And it’s the agreement that will win the greatest level of support.—

“I know [Baucus] is very interested in moving this,— said Sen. Debbie Stabenow (D-Mich.), a Finance member who often opposes free-trade agreements but believes the Panama pact is less controversial.

President Barack Obama has called on Congress to approve the deal, and U.S. Trade Representative Ron Kirk has said he’s working “fervently— to win passage by the end of June. But trade observers suggest the administration may only be giving lip service to the deal and is more interested in spending its political capital on getting Democratic votes to pass universal health care and global warming initiatives.

Some aides and lobbyists believe House Democratic leaders already have enough votes to pass the Panama agreement but are reluctant to press Members to make the vote until they pass bills this summer on health care and climate change. Both of those measures have raised concerns from moderate Democrats, and passing them could come down to a handful of votes.

“It bounces back and forth,— said Rep. Phil Hare (D-Ill.), a former union official who opposes most trade deals. “Some people say we want to do it right away.’ Others say, all three [pending trade deals] will go.’ Then I hear it’s not going to happen.—

Some House Democratic opponents have said they will not back the deal until Panama promises to step up its enforcement of international tax laws and add stricter labor and environmental provisions to the pact.

“The safe and honest way to say it is [negotiations] are still ongoing,— said Rep. Sander Levin (D-Mich.), who heads the Ways and Means Subcommittee on Trade and is leading negotiations on the labor and tax provisions.

Kind, however, cautions against making too many changes to the deal, first negotiated under President George W. Bush. “If some groups continually move the goal posts, I think that is unfair to the countries we’re negotiating with and also our own negotiators that won’t know what is or what is not politically acceptable.—

Bill Reinsch, president of the National Foreign Trade Council and a former undersecretary for export administration in the Commerce Department, said failing to approve the deal could harm U.S. relations in Central and South America. “If we didn’t do [the agreement], I think other governments are going to say, once again the Americans are sticking it to us,’— Reinsch said.

Observers on Capitol Hill and K Street say they have been surprised that labor opposition to the deal has been more muted than in the past. Thea Lee, policy director for the AFL-CIO, said the group was waiting to launch its opposition efforts. “We’re holding off until we see a timeline,— she said.