-Well sure, but that's no different than the current American system: A congressman represents his district, but also has to look out for the interests of his party because they'll be bankrolling his re-election campaign.
In general, you can expect the party to support an incumbent in any situation (unless they pull a Todd Akin and become so politically toxic that all is lost). And in primaries, if you have independent financial support and the voters like you, you can get elected as a Republican while announcing your support for child cannibalism and there ain't a damn thing they can do about it. What stops Ted Cruz from saying as he pleases? The party isn't going to support an opponent in the primary (not that they would succeed: he's beloved in Texas; perhaps not enough that he can go and support cannibalism, but beloved nonetheless), and there's no way they'd support a democrat over their own. This is all true of the democrats, but they've had more success with keeping people in line (and largely because of ideological and political factors, rather then financial).
And again, party discipline is a thing even in today's US.
Tell that to Speaker Boehner, I'm sure he'll be excited to hear it.
It exists plenty, but one consequence of the two party system is it is literally impossible to
always negotiate as a single bloc (or two single blocs): there are always issues on which you can peel away members. Some Congresspersons come from states that are absolutely committed to farm subsidies, others come from a small district and ran their campaigns entirely on "Let's bomb Iran", and still others come from a purple state that punishes misbehavior by switching parties. Mitch McConell is fighting Obama's proposed Coal regulations tooth-and-nail. But rather then being in the pocket of some company (directly, at least), it's because he comes from a coal-mining state that will
crucify him if he does otherwise.