A constitutional republic is where the people delegate certain powers, enumerated in a constitution, to the government. The Constitution of the United States defines three branches of government, the Legislative, Judicial and Executive. Ideally each branch serves to check the unrestrained power of the other branches (or two branches check the unrestrained power of the third.) That's what makes the revelations about mass logging of emails by the NSA, part of the Executive branch, so important.
> A constitutional republic is a form of representative democracy.
This is not generally true in the abstract, but the specific form of most Constitutional republics, including the US, is basically representative democracy, though sometimes (as in the US) with skewed voting power, and democratic values (coupled with fear of the volatility and excesses of direct or unconstrained democracy) was fairly central to the founding ideology of the United States.
No part of the US federal government is representative at this point. The Senate isn't by design, the house isn't because it's been capped, the presidency isn't by design.