They did to some extent, but not in all ways.
The main thing the Jacksonians did that upheld the spirit of the Constitution was to emphasize democracy. They helped to allow more white males to vote and encouraged participation by the "common man."
However, the Jacksonians did take some specific actions that did not guard the Constitution. For one thing, Jackson did not uphold the Supreme Court's decision on Indian Removal. In this way, he failed to support the Court, which has an important role given to it by the Constitution. In addition, Jacksonians banned abolitionist literature from the mails. This would seem to violate the First Amendment.