(CNN) From the start, US Trade Representative Robert Lighthizer has argued he can get Democrats to support President Donald Trump's replacement for the North American Free Trade Agreement. Now it's time to see if he can deliver.

Lighthizer appeared before the Senate Finance Committee on Tuesday and is set to testify before the House Ways and Means Committee on Wednesday. He is toutingTrump's revised trilateral trade deal, adding to the administration's efforts to pass the agreement over the summer -- a drive to secure key 2016 campaign promise heading into the 2020 campaign season.

He's up against fresh resistance after triggering consideration of Trump's US-Mexico-Canada Agreement on the same day that his boss issued a surprise threat of tariffs on Mexican goods last month, drawing rare outcry from Republicans . Members of both parties are also irritable over the looming possibility of national security tariffs on foreign cars and auto parts, which would hit the US operations of foreign manufacturers.

The list of people he hopes to sell includes members such as Connecticut Democratic Rep. Rosa DeLauro, who voted no on the original NAFTA and who issued a scathing statement trashing the USMCA last month. She's among the Democrats on a working group appointed by House Speaker Nancy Pelosi to piece together a deal with Lighthizer. The group, led by Ways and Means Chairman Rep. Richard Neal, also includes Reps. Earl Blumenauer, Suzanne Bonamici, Jan Schakowsky, Jimmy Gomez, John Larson, Terri Sewell and Mike Thompson, according to a House Democratic aide.

Trump has repeatedly suggested that if he can't get cooperation from Congress, he will withdraw from the 25-year-old pact, disrupting the global economy and deeply-entrenched supply chains, if Democrats don't ratify his replacement. Republicans have convinced Trump to stand down on scrapping NAFTA in the past. Such a move would likely trigger legal battles over whether Trump has the authority to unilaterally withdraw from trade agreements.

On Tuesday, Lighthizer will argue Trump's USMCA is already strong in key areas House Democrats have emphasized most — labor and environmental protections and enforcement — but he will also indicate openness to negotiating with lawmakers in drafting the implementing text of the deal.

"I am aware of specific areas where Members have ideas to strengthen the agreement, and we are having constructive discussions on how to make improvements," Lighthizer said in his opening statement. "My hope is that working with members, we can submit implementing legislation that Congress can approve very soon."

"I continue to believe that the USMCA will win broad support in Congress, as it is designed to do," he said.

Democratic lawmakers have slammed aspects of the USMCA, arguing it does not go far enough to ensure new labor and environmental protections are adequately enforced. Members have also taken issue with the agreement's pharmaceutical provisions, which would enshrine protections for biologic drugmakers by preventing cheaper alternatives for a decade.

Some, including Pelosi, have even called for the administration to reopen negotiations with Canada and Mexico in order to make substantive changes to the deal. The White House has rejected that idea, preferring to address any changes in the implementing text instead.

Talks between administration officials and Democratic leaders have repeatedly been strained by the President's unconventional trade strategies, including his threatened tariffs on Mexico, which drew fire from lawmakers of both parties.

Trump also didn't win any favor among Democrats when he took them by surprise two and a half weeks ago with the decision to pull a procedural trigger to allow the White House to move closer to congressional consideration of the deal after 30 days under Trade Promotion Authority.

After the 30-day clock expires next week, Trump will be able to send implementing legislation to Capitol Hill, although he could wait longer. Once his administration finalizes the legislation, it would kick off an expedited timeline, known as fast track, during which Congress would weigh the agreement.

Pelosi reacted to the White House's move with frustration, saying it was "not a positive step."

"It indicates a lack of knowledge on the part of the administration on the policy and process to pass a trade agreement," she wrote in a statement at the time.

Yet the speaker can push back on attempts to pressure her on the issue. In 2008, Pelosi used a procedural maneuver in the House to slow-walk a Colombian trade deal by stripping it of its fast track status. She could do the same thing with Trump's USMCA if Democrats aren't pleased by negotiations with the administration.

During the hearing, South Dakota Republican Sen. John Thune asked Lighthizer if he had a deadline for introducing implementing legislation if talks with Democrats break down. Lighthizer said the process was "ongoing, and I think we are making progress," but he declined to name a date at which the administration would proceed without an agreement with House Democrats.

"We certainly agree with you that we want this to be dealt with as soon as possible," he said.

Lighthizer's appearances come as the Mexican Senate is expected to take steps to ratify the agreement in the coming days. Leaders signed the USMCA last November, but it still needs to be ratified by all three countries.

Lighthizer also addressed the Trump administration's broader trade agenda, including references to goals like eliminating trade deficits and shoring up negotiations with Japan and the European Union. He took a shot specifically at the EU for its trade barriers to American agricultural products, arguing close trading partners may "agree with us on many important matters but do not always have the same level of ambition as the United States in securing a level playing field in international trade."

In one of the more tense exchanges of Tuesday's Senate hearing, New Jersey Democratic Sen. Bob Menendez pressed Lighthizer on Trump's unfulfilled threat to slap tariffs on all goods imported from Mexico. Lighthizer defended the ploy, arguing that in situations of national security, "you do what you have to do."

Menendez slammed the tactic and urged Lighthizer to push against similar threats in the future, saying it is "a dangerous economic game to play, especially when we're not talking about trade-related issues."

Senate Finance Committee Chairman Chuck Grassley praised the revised NAFTA in his opening statement for the hearing, as well as Trump's firm stance in his ongoing trade war with China and the administration's effort to open up European markets to American farmers.

The Iowa Republican also emphasized his longstanding disagreement with Trump's use of tariffs.

"I do not agree that tariffs should be the tool we use in every instance to achieve our trade policy goals. I fear that continuing to use tariffs in this way will undermine our credibility with our current and potential trading partners, and undo the benefits of our historic tax reform," Grassley told Lighthizer, in his opening statement.

"To be clear, American importers and consumers are paying for these tariffs," he added, pointing to current tariffs on Chinese goods as well as Section 232 tariffs on foreign steel and aluminum. "Taking nearly $22 billion out of the pockets of hardworking Americans is not in our national best interest."

The top Democrat on the committee, Sen. Ron Wyden, criticized the USMCA as insufficient and hit Trump for driving away American allies with his use of tariffs, adding that "there is no discernible strategy" in the President's behavior.

Wyden also said the more than $300 billion in additional tariffs Trump is considering slapping on finished Chinese goods would drive up consumer prices, hurting families as they go back-to-school shopping.

"As a result of this mismanagement on trade, the American people are faced with the prospect that everyday life in this country will become more expensive and less secure," the Oregon Democrat told Lighthizer.