The US as a constitutional republic was designed to frustrate that tendency. Recent calls for the repeal of the 17th amendment (senators used to be selected by state legislatures; that amendment made it popular vote instead) are based on that argument.
http://www.nationalreview.com/articles/252825/repeal-sevente...
Under the original arrangement, senators had strong
incentives to protect federalism. They recognized that
their reelection depended on pleasing state legislators
who preferred that power be kept close to home. Whereas
House members were considered representatives of the
people, senators were considered ambassadors of their
state governments to the federal government and, like
national ambassadors to foreign countries, were subject
to instruction by the parties they represented (although
not to recall if they refused to follow instructions).
And they tended to act accordingly, ceding to the
national government only the power necessary to perform
its enumerated functions, such as fighting wars and
building interstate infrastructure. Moreover, when the
federal government expanded to address a crisis (such as
war), it quickly retreated to its intended modest level
after the crisis had passed. Today, as historian Robert
Higgs has observed, federal expansion creates a “ratchet
effect.”
Just as important as its role in securing federalism, the
Senate as originally conceived was essential to the
system of separation of powers. Bicameralism — the
division of the legislature into two houses elected by
different constituencies — was designed to frustrate
special-interest factions. Madison noted in Federalist 62
that basing the House and Senate on different constituent
foundations would provide an “additional impediment . . .
against improper acts of legislation” by requiring the
concurrence of a majority of the people with a majority
of the state governments before a law could enacted. By
resting both houses of Congress on the same constituency
base — the people — the Seventeenth Amendment
substantially watered down bicameralism as a check on
interest-group rent-seeking, laying the foundation for
the modern special-interest state.