On the contrary, I think they'd have problems initially due to the suddenness and mystery of the threat - after all, despite what the movies suggest, if an outbreak ever did occur, we really wouldn't know what to do because it never happened before, at best we can only speculate.
Once this obstacle was overcome, I think the zombies would be defeated - but not after a long, drawn-out battle.
In reality, the real problem is the initial shock factor - coming to terms with the rapidly evolving menace. Not being able to initially confront it is what causes danger - because the threat grows exponentially to the point where you have a massive army of zombies to deal with.
I think, initially, they would try to deal with it themselves and possibly be effective for a time, but there will always be that one zombie who runs out onto the street and blows everything to smithereens.
if they were to act they would go after vauable resources and save their own economy such as keeping huge banks, also they would go after people who has obtained alot of poltical power such as henry kisinger, and the rockefellers, in huge citys like new york they will simply save the cargo and umbanded the ship, worse case senerio launch a nuke, the miltiary would most likely quartine major citys the national guard and navy would do the same, but if your talking about in the u.s since obamas sending more troops in the mid east even more than bush I would see UN troops and other foriegn troops on our soil then we would lose our soverignty and the u.s government will fall apart and their land will go to trusted allys like the european union then the outbreak will go after the enite world in the same fasion I just explained over and over untill the world is infected.
also in additon to what I have explained this will go on untill the richest and the most powerfull country or union currently in the world is left and will give the duty for a one world government which will be the last one left until the infection had wiped everything off the planet
The govenment have a plan incase no one here is intrested enough to look it up, witch im suprised about considering this is a site all about zombies. Dr Smith? (the ? at the end of smith is not a mistake its actuly how his name is written) came up with the plan Dr Smith?'s plan is when the outbreak is known about by the government, they will bomb that particular city or contry with no regard for casualties because of the sevearty of the situation of zombies and potential world zombification so there ya have it they may not be very pleasent but there not rely looking after number 1 there they do have some compation there human just liek you and me