Thanks for the input,
I failed to mention in my original query that during this strange
behavior the check engine light never illuminated to signal that a code
condition had occurred.  With that said, I'm going to try and see if one
of the local auto parts shops will take an ODM reading to be sure.

Thanks again for your thoughts.

You're probably fairly safe to relax on the idea that this is a major
problem or a warning that you're about to have a timing belt problem.
It's much more likely that this is an ignition, sensor, or fuel delivery
issue.  

Additionally, timing belts tend to fail suddenly with no advance warning.
With either of the engines available in the Tucson, there's a near zero
probability that the belt will fail prior to the replacement interval.

The extended crank is often caused by a fuel pressure regulator which
dissipates all the fuel pressure when the vehicle is off.  But this rarely
causes a stumbling once started.  It's also possible that the issue was an
incorrect fuel mixture due to erroneous coolant temperature sensor
readings.  And it's possible that there's a spark plug, plug wire, or
ignition coil issue.

You might stop by AutoZone or similar place just to see if any codes
stored but did not turn on the check engine lamp.  If so, this may provide
further hints as to what the issue was.

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Hyundaitech, you provided some much-appreciated comments on timing belt
changes for my 2005 Tucson (which I'm rapidly approaching with 59,300
miles so far).

I had a rather disconcerting occurrence today that I'd like to better
understand.  When cranking, the normally one-time ignition turn took
four tries.  I passed it off as something I did.  However, once out on
the street my vehicle was struggling and sputtering along.  About two
blocks away from my house the Tucson died.  I was able to start it back
up and it ran fine afterwards but made me start to question what would
cause such strange behavior.

Is this the symptoms of a failing timing belt or other such problem or
is it related to transmission problems.  Or, hopefully, could it just be
 fouled fuel filter or bad batch of gas???  Hoping for the latter but
would like to avoid the former, where more costly repairs could come
into play if I don't hightail it to the mechanic now.

Thanks in advance.

Ken