They always anticipated the need for a 'landing abort' - and it was practiced endlessly in the simulator in Houston. Had the descent stage fuel gotten critically low, Houston would have called for a landing abort since they assumed the LM would be under active control when the abort occurred (and if they ran out of fuel the LM would instantly become uncontrolled). Not saying they couldn't have successfully aborted after fuel exhaustion, but it would have been even more difficult. That being said, it was later determined that they had more fuel left than they thought (not sure how they determined that, it's not like they could go check the tanks...).
There always was some concern that a landing abort - especially at very low altitude - might not be successful. No one knew just how accurate the LM simulator really was. Apparently - at least for the maneuvers they actually performed - it was pretty darned good since the astronauts reported later than the real thing was actually easier to control than the simulator (and much easier than Lunar Landing Research Vehicle (LLRV) - of which they crashed several). If they needed to abort, the lightoff of the ascent stage was pretty much instantaneous - if you've ever seen the footage of the Apollo 17 liftoff from the moon, it gives you an idea of just how sudden the ascent motor comes on.
But the whole Apollo 11 landing was a pretty nerve racking affair - and the extra time that Neil spent looking for a good landing spot just added to the suspense.