House Ways and Means Chairman Richard Neal, who leads the nine-member USMCA working group, called the letter a "significant step in the right direction" but maintained there is more work to be done on the issue.
"There is still fluidity on the labor stuff and enforcement," Neal told reporters. "So we're looking for more assurances."
Neal spoke after a roughly 90-minute meeting between the working group and U.S. Trade Representative Robert Lighthizer - the trade official's second of three scheduled visits to Capitol Hill this week.
The group has been working for months to negotiate changes to the deal in four main areas: enforcement, labor and environmental standards and drug pricing provisions.
The administration and lawmakers' staff members worked throughout the two-week congressional break in an effort to get closer to a deal. Asked whether the two sides might be able to reach a handshake deal by Thanksgiving, Neal replied: "I would like to think that, but I think that even based on what we discussed here today ... that there's still a ways to go."
Lighthizer is scheduled to meet with the group again on Friday morning to keep pushing toward a deal, Neal said.
Pelosi, who met briefly with the working group on Wednesday, added that Democrats are "not there yet because we don't have the enforceability assurance that we need to have."
The Trump administration, Republicans and business groups have increased pressure to have USMCA put to a vote in Congress this fall. Democrats have said they hope that they'll be able to get a deal done this year despite the ongoing impeachment inquiry.
Pelosi also dismissed President Donald Trump and Republican leaders' claims that the impeachment inquiry is stopping Congress from getting work done.
"The people who are saying that don't know what they're talking about or have a different agenda that they want to present," the California Democrat said.
Neal also praised Pelosi for saying "from Day 1" that she wants to show Democrats can still govern even as the impeachment investigations proceed. The trade deal, he noted, "is one of the best vehicles" for proving that Democrats can do both.
And even though some concerns remain, the Massachusetts Democrat said the "one truth" in place is that "what we have already done is better than what NAFTA represents at the moment."
"That is not in dispute," Neal said. "The question is can we move it along even more, and I think we can."