WASHINGTON (AP) — The Senate's top Republican on Tuesday pleaded with lawmakers to move ahead on a trade bill that has the strong backing of President Barack Obama but faces fierce opposition from several rebellious Democrats.

"Let's vote to open debate on a 21st Century American trade agenda," Majority Leader Mitch McConnell of Kentucky said on the Senate floor, hours before a test vote. "Let's not slam the door on even the opportunity of having that debate."

The bill needs 60 votes in the 100-member Senate merely to start a full-blown debate on the legislation that would grant Obama "fast track" authority. He could then present Congress with proposed trade agreements it can ratify or reject, but not amend. If successful, he's likely to ask Congress to approve the Trans-Pacific Partnership being negotiated with 11 other countries, including Japan, Vietnam, Canada and Mexico. Other free-trade proposals could follow.

But several Democrats demanded that McConnell deal with surveillance and highway issues first.

Obama's stiffest resistance is from fellow Democrats who say trade deals take away U.S. jobs. Most Republican lawmakers support trade agreements. But at least some of the 54 GOP senators appear poised to oppose the president Tuesday, requiring him to hunt for perhaps 10 Democratic supporters.

Several Democrats say they will back fast track only if Republican leaders clear a path for three other trade measures. One, to renew the African Growth and Opportunity Act, is uncontroversial.

The second calls for Trade Adjustment Assistance, which provides federal aid to workers displaced by trade agreements. Republicans don't like it, but reluctantly acknowledge it's the price for winning even modest Democratic support.

The third bill, involving Customs enforcement, is the stickiest. It includes a measure to take actions against countries that keep their currency artificially low, which makes their exports more attractive. The Obama administration opposes the "currency manipulation" measure, saying it could invite international challenges to the Federal Reserve's policies meant to boost the U.S. economy.

McConnell said that only two of the bills — fast track and Trade Adjustment Assistance — would be the subject of initial votes, but senators would have ample chances to address the other two bills during the amendment process.

"The bill we'd be voting to proceed to is simply a placeholder that will allow us to open the broad debate on trade our country needs," McConnell said.

Democrats urged McConnell to make a more clear-cut path for all four measures to become law. "It's going to be very difficult" to move forward on trade if he doesn't, said Senate Minority Leader Harry Reid, D-Nev., who opposes fast track.

Lobbying for and against Obama's trade agenda hit overdrive this week. Key groups scheduled almost hourly events on Capitol Hill ahead of Tuesday afternoon's scheduled vote. Obama devoted much of the weekend to trade, visiting a Nike plant in Oregon.

He pointedly criticized a leading Democratic foe, Sen. Elizabeth Warren of Massachusetts, in an interview with Yahoo News. Several Democrats said the remarks irritated colleagues who are weary of seeing the president cozy up to Republicans on trade.

Obama maintains that U.S. goods and services need better access to the 95 percent of world consumers who live in other countries.

Democratic opponents urged wavering colleagues to vote against McConnell on Tuesday, even if they might support fast track in the end. They want to force Republicans to deal first with a surveillance measure that Democrats consider more pressing. That strategy suggests Obama might have better luck on trade in a month or so, should he fall short in Tuesday's vote. But that clearly is not the White House's preference.

Pro-trade and anti-trade groups flooded websites with reports, polls and arguments for their sides. The U.S. Conference of Mayors held a conference call to support Obama on fast track. The conservative group Heritage Action for America declared that Trade Adjustment Assistance "undermines free trade."