While the US Constitution does not prevent fractiousness (no constitution can), it can limit fractiousness by seeking to make the American government more broadly representative than just simple majority rule. Pure majority-rule democracy was widely regarded by the Founding Fathers as a direct threat to the rights of the minority, so they put safeguards into the constitution to protect certain key rights of all Americans, regardless of who was voted into power by the majority. This was meant to prevent the majority from tyrannizing and oppressing the minority.
The Constitution thus reduces fractiousness in creating a system more broadly representative by making sure the voice of the minority is taken into account and not just that of the majority. One way it achieves this goal by having two houses of Congress. If the Founding Fathers had wanted simple majority rule, they could have had 535 legislators in one chamber, in which a majority would be sufficient to pass new legislation. Instead, they gave us a Senate, in which 51 members could block the votes of the other 49 Senators as well as all members of the House, providing a major check on a potential "tyranny of the majority."