Lets give some more information.
The International Earth Rotation and Reference Systems Service (IERS, http://www.iers.org) has been measuring the Earths rotation since 1988. They found that the earths rotation is not constant but changes because of various factors. One of those are the tides. The tides are believed to slow the earth's rotation down a bit.
This cannot be measured in "earth-time" because there are always 86400 "earth-seconds" in a day, no matter how long or short the day is. It is so by defenition.
It can be and is measured by atomic time though. The results are that our days are getting several milliseconds longer every day. This adds up to about one second per year. (years get one second longer every one or one and a half year) To compensate this leap-seconds are inserted.
So it seems as like days were shorter in the past. I am not sure if the data goes that far back, but it seems like it.
Shorter days might also be a possible explenation for the higher measured speeds of light in the past.
So to summarize: the data is there, now lets interpret it without trying to keep our precious theories intact(, right tuppence?)