Not really. The constitution was born out the ideas of laissez-faire liberalism (not to be confused with new liberalism) which only has loose connections to modern conservatism (think modern economic conservatism without supply-side Keynesian economics and social conservatism). Social conservatism seeks to use the government to enforce its specific view of morality on the populous for better or worse. This is opposed to the ideas of laissez-faire liberalism which idealizes individualism and negative liberty. You cannot ascribe modern political labels to older documents as they are generally not inline with each other.