In some ways he has rejected Bush's approach. He ended the use of torture (notably waterboarding) on enemy captives and closed down the CIA's secret prisons. In other matters related to personal freedom, he's been a welcome contrast to Republicans -- endorsing the mosque near Ground Zero, abolishing the military's ban on openly gay members and supporting same-sex marriage.
If you're looking for an opponent willing to call Obama out for his disappointing efforts in this realm, Mitt Romney is not the candidate for you. When it comes to civil liberties, he gives every appearance of being Dick Cheney without the charm.
Close Guantanamo and transfer the inmates? Not a chance. In 2007, Romney said, "I want them on Guantanamo, where they don't get the access to lawyers they get when they're on our soil. ... My view is we ought to double Guantanamo."
When it comes to torture, the only time he says "no" is when he's asked if he's had enough. Last year, his campaign spokeswoman said Romney does not regard waterboarding as torture and declined to say he would not use it.
Another difference between the two candidates involves the Supreme Court, where neither would be ideal. Obama bitterly rejects the court's view that corporations have a free speech right to spend money on elections. His Supreme Court appointee Sonia Sotomayor signed a dissent concluding that despite the Second Amendment, "the use of arms for private self-defense does not warrant federal constitutional protection from state regulation."
The person Romney chose to head his Justice Advisory Committee is Robert Bork, whose 1987 Supreme Court nomination was rejected largely because of his evident contempt for judicial enforcement of the Bill of Rights. After Bush was criticized by the ACLU and others for his aggressive post-9/11 anti-terrorism measures, Bork said Bush deserved criticism -- "for not going far enough."
That's the sort of sentiment that rarely gets a candidate defeated. Right now, we don't know whether Obama or Romney will come out on top in the election. But it's a safe bet that civil liberties will not.