Part of the reason for having two houses of Congress is that it places an obstacle to majority rule. Fifty-one senators can block the wishes of 435 representatives and 49 senators. The Constitution gives the president a veto to thwart the power of 535 members of Congress. It takes two-thirds of both houses of Congress to override the president's veto.
In Federalist Paper No. 10, James Madison wrote, "Measures are too often decided, not according to the rules of justice and the rights of the minor party, but by the superior force of an interested and overbearing majority." That's another way of saying that one of the primary dangers of majority rule is that it confers an aura of legitimacy and respectability on acts that would otherwise be deemed tyrannical. Liberty and democracy are not synonymous and could actually be opposites.