Bachmann is crazy for all sorts of reasons, and she goes too far here, but she is on the right lines. Indeed, Merkel, Cameron, Sarkozy and all sorts of other leaders have made speeches saying more or less the same thing.
Western culture offers a better way of life, moral code, and societal norms than many other cultures. That is not to say it is not without deep problems, nor that we cannot learn from others - but we broadly have the right values, and we should certainly make adherence to those values a test for anyone who wants to settle here.
It is not just the obviously barbaric practices which are the problem. (Though it should be said that there are some on the left, such as Ken Livingstone, ready to embrace extremists like Sheikh Qaradawi, even though he supports female mutilation and all sorts of other evils, in the name of multiculturalism). It is the wider sense amongst some (perhaps large subsections of) cultures that they are not "part", that they can be distinct, together with a desire to force Britons to adopt their own, often rather abhorrent values - attitudes deeply rooted in the culture of the societies in which they originate - which is at the root of the inevitable failure of multiculturalism.
Of course, it is possible to live in isolation in the West if you do it quietly and without causing fuss - hence, no-one cares about the almost Amish-style lifestyle of certain orthodox Jewish communities.
Ultimately, it is about values. The positive aspects of having so many different people from so many difference places are self-evident - the cuisine, the dance, the music - and indeed, we should welcome these positive aspects of exposure to different cultures.
However, we should not let these things fool us into believing multiculturalism is a success, in terms of societal cohesion, for a second. These benefits are largely confined to a narrow section of the middle class.
Not all values are equal. We should be far more vocal in saying so.