The Democratic nominee was asked to address 46's controversial comment Wednesday morning ... after Biden faced flak for implying Trump supporters are "garbage" Tuesday night -- a callback to a similar remark that was made about Puerto Rico at DT's rally at Madison Square Garden on Sunday.

While the White House has tried to walk back Biden's gaffe -- emphasizing the prez's comment was only about comedian Tony Hinchcliffe, who made the PR dig -- Harris said she would not stand for criticism of Trump's supporters.

She told reporters ... "I strongly disagree with any criticism of people based on who they vote for. You heard my speech last night, and continuously throughout my career. I believe that the work that I do is about representing all the people, whether they support me or not."

As she continued, Harris emphasized it was her "responsibility" to be a leader for all, noting she takes her job "very seriously."

When asked if she was concerned about the impact Biden's comment may have on voters, the Presidential hopeful indicated she was unfazed by the hiccup ... saying she's been very clear with voters about her plans for the Oval Office.

She added ... "I respect the challenges that people face. I respect the fact that we all have so much more in common than what separates us, and that most people want a president that understands that."