In the gospels, Jesus says he is the master of shabbat; how can a person be a master of something he is abolishing?
Again in the gospels, we read Jesus ruling it is lawful to do good on the sabbath - if he was aiming at abolishing sabbath, why talk about what's lawful to do during sabbath?
Then, in the epistles, the author of Hebrews writes, "There remains a Sabbath rest for the people of God."
Combined with the historical reality that the early Christians were almost all Jews who saw themselves within Judaism, it is probable the early Christians were sabbath keepers.
As others in this thread have noted, spiritual significance aside, the physical rest and ceasing of ahabbat is healthy. Its importance is amplified in our work-obssessed culture; more so in the startup culture.