Does being for less immigration mean a party is inherently right-wing?

[rob in cal]

   The politics of immigration, both in the US and elsewhere is, for me anyway, endlessly fascinating.  I love how big business and the left are united on this one issue.  What I've noticed is that whenever a candidate or a party proposes a big reduction in existing legal immigration that party or candidate is usually identified as right wing, even if the rest of the politics about that party or candidate isn't inherently right wing.
    I think Pim Fortuyn in the Netherlands and his party is a great case.  He was against immigration of Moslems into the Netherlands because he felt they were a threat to the continued existence of a socially liberal society, IIRC. 
    Bill Clinton tapped liberal Democrat Barbara Jordan to chair a study on the overall impact of immigration into the US, back in the 90's, and the commission ended up calling for less immigration, though in that case I don't believe Jordan was labeled right wing.
    If an otherwise liberal Democrat came out for less immigration would they still be a liberal Democrat?
    In Europe it seems like a lot of the less immigration parties, like the Progress and Peoples parties in Norway and Denmark are called right-wing, even though the rest of their platforms don't seem very right wing.  Perhaps it is a matter of style, in that the British Conservatives have called for very significant immigration reductions (not sure that its happened since Cameron has become PM though), without the Tories being labelled an imminent threat to freedom and democracy.