It would be an overstatement to say with any kind of certainty that "the broader Democratic Party agrees", whether you are asking about elected officials or the base, nationally or locally. There can be no certain answer, as I'm seeing no relevant public opinion poll, and no specific bill that has been voted on.
However, what we do know is that Norton is not entirely alone, but opinion on this is mixed at best. Here is a relevant article which includes the following:
“The meaning is degrading,” said Marcus Goodwin, a candidate for the District of Columbia Council. “To see my ancestors at the feet of Lincoln — it’s not imagery that inspires African-Americans to see themselves as equal in this society.”
Mr. Goodwin has led calls for the memorial, also known as the Freedman’s Memorial, to be taken down through a legal process, including a petition that prompted Representative Eleanor Holmes Norton, Democrat of the District of Columbia, to announce she will introduce legislation before the House of Representatives to remove the memorial.
Most of the other people quoted in this article are not supportive. As I write this, the petition is currently approaching 7,000 signatures which is modest but not insignificant, especially if we consider that this is primarily an issue of interest to local residents.
As a final note, I will mention that a very similar statue in Boston will be removed. The relevant commission voted unanimously to do so. Another in Madison, WI has also seen some controversy, but as it does not depict a black man on his knees, there may be less support for removing it.
