When the the US invaded Iraq, I started to doubt my own firmly held beliefs. Did they possess some classified evidence that I did not? Going to war without the authorization of the Security Council was such a grave breach of precedent and international law that I didn't believe the Bush administration would take such a drastic action if they didn't fully expect to find WMDs.
It turns out they didn't secretly have reliable information the rest of us didn't. They were blinded by conviction and ideology.
I'm sure these people in government and at the intelligence agencies truly believe these programs are vital to protect the US from terrorism. They know spying can be abused, but in their minds any abuse is unintentional and minor relative to the purported benefits of spying on terrorists.