Believe it or not, I'm actually AGAINST the death penalty
(mainly because I fear executing someone who may have been innocent).

But there are currently over 2 million people in prisons in the U.S.,
and the cost to taxpayers for such incarceration must be staggering.

Have there been any serious discussions among experts about the idea
of executing "career criminals" (assuming we can agree on the 
precise definition of "career criminal")?

I'm not an expert in this subject at all, and I'm probably very naive,
but I do see some benefits to the idea:
(1) Fewer people incarcerated, therefore a reduction in tax dollars.
(2) A stronger deterrent to future career criminals.
(3) Innocent people would not be executed (because they are not
    career criminals).

My definition of a "career criminal" (for the sake of argument) would be
someone who:
(1) Has been convicted at least 5 times for different unrelated crimes.
(2) Has spent at least 50% of his adult life in prison.

The official answer to this question should provide references to written
material (both pro and con) by respected experts.

SHhhh!  We don't talk about that!  

The Politically Correct (PC) assumption is that criminals are supposed
to be rehabilitated so that they can return to society as good
citizens  - but comments to a few questions here have indicated that
this is really extremely difficult, since it is virtually impossible
to get a job with anything on one's record, and these days it can't be
hidden.

You may have heard of California's "three strikes and you're out"
policy:  life imprisonment for anyone with a third criminal conviction
 - of any kind.  This is, indeed, a very expensive approach, but at
least it admits that taking criminals out of circulation to protect
society is a principle, and that the threat of life imprisonment could
be a deterrent.  The problem is that a released criminal after two
convictions has no practical chance of "returning to society."  He/She
needs to be deterred before his/her career even starts.

PC is to consider that the punishment should fit the crime and that an
excessive  punishment is no deterrent, extreme case:  the death
penalty does not stop people from murdering.  This is true, but for
lesser crimes, the threat of massive punishment could be a deterrent.

It is felt that Islam's Shariah laws are excessive  - cutting off the
right hand for thievery -  but maybe it is a deterrent.  (Statistics?)

Myoarin