Does the creative "spoken word" of Jesus (e.g. Luke 18:42) demand a Young Earth Fiat Creation interpretation of Gen. 1:1?

do the bible verses in the N.T. and the O.T. demand a real week of time as we know it?

Absolutely not. If anything, they argue against a week. A number of prominent theologians in the early Church believed that a week is too long, and that Creation was accomplished in an instant.

It may well be that Creation took no more than a few instants. What seems likely, however, is that such instants were deliberately spread out. The reason, for this, can of course be seen in Exodus 20:11 (and elsewhere). "For in six days the Lord made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy." Spreading Creation out over six days was a very deliberate act that God used to set a model for humans.

It should also be noted that, in order for that model to make sense, the days of creation must be actual days, not long periods of time. Of course, given that God can and does accomplish things in incredibly short periods, insisting on inserting thousands, millions, or even billions of years into Creation is to insist that God can't accomplish such miracles, in such manner and in such short intervals, as are recorded in the Gospels.

As to whether these miracles happened in an actual instant (perhaps something resembling a Planck second) or simply a very short period of time, it's worth keeping in mind that God is outside of time, and is all-powerful. It makes sense that something God ordains would simply be, unless He had a specific reason for causing it to happen more slowly.

Is this one of the major reasons Christian Young Earth Creationists accept a short time (not billions of years) for their interpretation of Genesis 1?

I would say it's definitely a reason. Whether it counts as "major" might be a matter of opinion. Personally I feel that the main reasons for believe in a "young" (~6ky) Earth are:

• The various chronologies and genealogies (Genesis 5, Luke 3) don't appear to leave any room for longer spans of time.
• There does not appear to be any scriptural reason to believe that Genesis 1-11 is not intended to be taken as straight-forward history. (This is not to say there isn't additional, spiritual meaning, but that the apparent historical meaning should not be rejected.)
• Jesus' own words place humanity at "the beginning" of Creation. This is directly in conflict with assertions that humans only showed up "recently".
• 2 Peter 3:3-7 seems to be speaking directly against those who would reject a historical reading of Genesis 1-11.
• Non-historicity of Adam is argued to have severe theological consequences.
• Belief in death before sin is argued to have severe theological consequences.
• Rejection of the historicity of Genesis 1-11 seems to open the doors for rejecting the historicity of any other part of Scripture... up to and including the Crucifixion and Resurrection, at which point one might as well reject all of Christianity.

That God clearly can accomplish things quickly, even "instantaneously", is certainly another reason. Additional reasons include:

• The available scientific evidence is argued to be more consistent with such an interpretation, while many lines of evidence are not consistent with millions or billions of years.
• Philosophical Materialism (that is, the belief that neither God not anything else spiritual exists, which is made possible by belief that Creation can be explained without reference to God) seems to have serious moral consequences which are clearly ungodly. (Consequently, from a Christian perspective, there is reason to believe that the battle between Creationism and Materialism is not merely about whose "science" is more correct, but may in fact be dominated by spiritual, or at least philosophical, conflict.)

Would they reason that it is stretched out to a 7 day week to give the man He was about to create an example of a salubrious work week?

Yes. As noted above, that seems to be the most obvious reason why God would "take His time".