Most objections to surveillance are not to all forms of government surveillance, instead people are objecting to extra-legal, and arguably illegal, mass surveillance. Those opposing mass surveillance tend to argue along some subset of following lines:
1. it is ineffective compared with other techniques,
2. it is government graft to favored contractors,
3. mass surveillance databases and collection points provide an excellent target for foreign intelligence agencies and others,
4. it is harmful to privacy and liberty,
5. it is rife for government abuse and blackmail,
6. it undermines the rule of law.
I have yet to see anyone argue against lawful and warranted targeted surveillance of known terrorists. I claim that none of the above objections hold in the targeted surveillance case.