Here is an argument made by the creationist Kent Hovind:
Did you know we have a leap-second about every year and a half now because the earth is slowing down?
Hovind calculates that if the Earth is slowing down by one second every 18 months (because a “leap-second” is added to clocks that often) then the Earth was spinning infinitely fast if the Earth was even a few million years old!
The answer to this is quite funny – and explains why even most creationists don’t use this argument. The addition of “leap seconds” to clocks is not a sign that the Earth is slowing down any more than adding “leap days” to the calendar during “leap years” is a similar sign.
We all know that leap days are added during leap years because the length of a year is not an integral number of days. They are not added because the Earth is slowing down by one day every four years.
Leap seconds are added for a very similar reason. Effectively they are added to allow atomic clocks to align with the Earth’s rotation. Here's how the US Naval Observatory explain this: at
"Confusion sometimes arises over the misconception that the regular insertion of leap seconds every few years indicates that the Earth should stop rotating within a few millennia. The confusion arises because some mistake leap seconds for a measure of the rate at which the Earth is slowing. The 1 second increments are, however, indications of the accumulated difference in time between the two systems. (Also, it is important to note that the current difference in the length of day from 86,400 seconds is the accumulation over nearly two centuries, not just the previous year.) As an example, the situation is similar to what would happen if a person owned a watch that lost 2 seconds per day. If it were set to a perfect clock today, the watch would be found to be slow by 2 seconds tomorrow. At the end of a month, the watch will be roughly a minute in error (30 days of 2 second error accumulated each day). The person would then find it convenient to reset the watch by one minute to have the correct time again."
"This scenario is analogous to that encountered with the leap second. The difference is that instead of setting the clock that is running slow, we choose to set the clock that is keeping a uniform, precise time. The reason for this is that we can change the time on an atomic clock, while it is not possible to alter the Earth's rotational speed to match the atomic clocks! Currently the Earth runs slow at roughly 2 milliseconds per day. After 500 days the difference between the Earth rotation time and the atomic time would be 1 second. Instead of allowing this to happen, a leap second is inserted to bring the two times closer together."
Basically a second is added to the clock every 18 months in order to align integral seconds with the Earth’s rotation about the sun without constantly losing time! Leap seconds have nothing whatsoever to do with any slowing of the rotational speed of the Earth.
Actually the Earth is indeed slowing down, just not at the rate suggested by the use of “leap seconds”. Instead it is slowing by about 0.005 seconds per year per year. When the Earth was formed about 4-1/2 billion years ago a single day took about 14 hours. That’s fast, but not close to infinite.
That means that the Earth’s rotation has not always been exactly what it is now. But the Earth has not always been slowing down at the rate that it is currently slowing down..
“...the correct present rate of slowing of the earth's rotation is excessively high, because the present rate of spin is in a resonance mode with the back-and-forth motion of the oceans' waters in the ocean basins. In past ages when the rotation rate was faster, the resonance was much less or nonexistent, resulting in a much more gradual slowing of the rotation rate. The most recent calculations indicate that the earth could be 4 to 5 billion years old and not have been spinning excessively fast or requiring the moon to be any closer to the earth than 225,000 kilometers (140,000 miles).”
So, even 14 hours per day is probably too low. Surely none of this presents any sort of problem for people who accept a multi-billion year old Earth.
 http://www.arrivalofthefittest.com/seminar1.html, referenced on June 19, 2008
 http://maia.usno.navy.mil/eo/leapsec.html, referenced on January 30, 2009
 http://en.wikipedia.org/wiki/Leap_second, referenced on June 19, 2008
 Thwaites, William and Frank Awbrey. 1982. "As the World Turns: Can Creationists Keep Time?" Creation/Evolution, Issue IX (Summer 1982), pp.18-22 National Center for Science Education, p. 19.
 http://www.talkorigins.org/faqs/hovind/howgood-yea2.html#proof20, referenced on June 19, 2008
 Sonleitner, Frank J. 1991. An Evolutionist Goes to the Creationist Movies 2 computer diskettes; 23 files National Center for Science Education.