How do I convert an interval into a number of hours with postgres?

Probably the easiest way is:

SELECT EXTRACT(epoch FROM my_interval)/3600

If you want integer i.e. number of days:

SELECT (EXTRACT(epoch FROM (SELECT (NOW() - '2014-08-02 08:10:56')))/86400)::int

To get the number of days the easiest way would be:

SELECT EXTRACT(DAY FROM NOW() - '2014-08-02 08:10:56');

As far as I know it would return the same as:

SELECT (EXTRACT(epoch FROM (SELECT (NOW() - '2014-08-02 08:10:56')))/86400)::int;