Was Calhoun or Jackson more attuned to the ideas of Thomas Jefferson?
I respectfully disagree with the above post, as it is just a matter of historical opinion. In 1799, Thomas Jefferson and James Madison were responsible for the passage of the Kentucky and Virginia Resolutions, which proclaimed the right of the states to reject any federal law they felt was unconstitutional. This is essentially nullification in its earliest form, but for a different reason. This was a reaction to Adams' Alien and Sedition Acts, which were clearly unconstitutional. The Supreme Court was made up of Federalists at the time, so they had not yet taken action to rule laws unconstitutional yet, and would not do so until 1803 and the Marbury v. Madison case.
So I think Jefferson would have sided with Calhoun on the issue of nullification. While he did develop more federalist leanings when he became President, I think at his core he was still a champion of the states.
I will assume that you are talking about the conflict between these two men over the issue of nullification, since that is the main time their two views could be contrasted.
In my opinion, Jefferson would have sided with Jackson in this conflict. While Jefferson was an anti-federalist, he was also a nationalist of sorts -- e put the good of the country before political principles.
For example, you can see this in his actions on the Louisiana Purchase. He was not convinced that it was constitutional, but he thought it was good for the country, so he did it.
I think you can see this in his imposition of the embargo as well -- that was similar to the tariff in that it hurt parts of the country, but Jefferson thought it was best for the country so he did it.