This question, or something similar, has been put to White House Press Secretary Jen Psaki a number of times over the past couple of months. The common theme of the responses is that VP Harris' brief is more to do with addressing the root cause of migrants arriving at the border at the source - by engaging with political leaders in Northern Triangle countries (Guatemala, Honduras, and El Salvador), as well as Mexico. The Press Secretary has also dismissed criticism of the lack of border visits as "political games", and has repeatedly emphasised that the administration is more focused on "solutions".
Firstly, on April 14th, Psaki was asked why VP Harris' first trip abroad, to Guatemala and Mexico (mentioned in Machavity's answer) wouldn't take in the border. In her reply, Psaki defends Harris' itinerary, and makes the point that border visits have been carried out by other members of the Biden administration:
Well, what the President has asked the Vice President to do is run
point on the Northern Triangle and be a high-level conduit in having
discussions with leaders in the region. That’s exactly what she is
doing and will do when she goes and visits countries in the region.
And obviously, she’s had discussions, that have been read out, as
well, with some leaders in the region.
Secretary of Homeland Security has visited the border. Our Secretary
— other secretaries who run point on these issues will and, we expect,
will in the future.
More recently, on May 12th, Psaki responded to a journalist who repeated the pleas of a couple who rescued five migrant children for Biden to visit the border:
Our focus remains on solutions, on ensuring we’re expediting
processing, we’re getting kids into safe and humane conditions, and
that’s — if going to the border changed that or helped that, that
would be one thing. But our focus is on implementing pieces that we
can — so we can make their lives better.
Finally, on May 14th, a journalist pointed out criticisms of President Biden and VP Harris' lack of visits to the border. Psaki reiterated her earlier point, saying that the administration is focused on solutions - and makes the point that some statistics at the border have been improving to justify this approach:
Okay. Well, the President’s focus and the Vice President’s focus is
on solutions. And what our — what we’ve seen over the past several
months is that, while we came in and there were — was little
preparation for what was going to be a surge of migrants at the
border, what we’ve done since then is rapid — or is massively reduced
the number of children who are at Border Patrol facilities from over
5,000 to under 1,000 — the pro- — the number is probably even lower
than that now — and massively reduced the number of hours that these
children are spending in these facilities.
So, our focus is on
working in — through the interagency process, pressing to eliminate
bureaucracy, and making sure that we’re taking steps that treat them
in a humane and moral way. And we’re less worried about press
conferences or political games that are being played by some.