This offensive is directed against Helmand province a Taliban stronghold. The US is using a new strategy. The intent is to clear and then hold areas. Earlier offensives by British and Canadian troops cleared an area but then moved out. When they moved out the Taliban moved back in.
One thing is certain and that is that there will be more US casualties. The Afghan war could in time make Obama unpopular as happened with Bush and Iraq. This offensive is targetting only two districts that are in a river valley that produces a great deal of opium. Although the US claims that it will no longer carry out poppy eradication it is not clear what is to happen to the crops in Helmland. Are they to be expropriated by McChrystal and used for special forces operations ;). Certainly the promotion of legal crops faces an uphill battle when poppy growing is so much more profitable. Also, it is not just the Taliban that profit from opium but many Afghan politicians as well as the farmers themselves. One can expect that there will be many attacks on the US forces trying to occupy and hold these areas. Meanwhile public opinion even in the US is not all that favorable to the war and outside the US only countries such as Israel show much support. Most of Europe has large majorities against the war and even in Canada a majority do not support the war. The US is finding it difficult to recruit more NATO country troops to join battle in Afghanistan although Pakistan armed forces are fighting Taliban in Pakistan more than previously.
http://en.wikipedia.org/wiki/Internation
Here is a recent article on the US offensive: