I think you should start with immortalized cell lines and so in vitro division rates by perfect conditions. This is easier to measure than in vivo division rates. E.g. HeLa has a division time of 23 hours. MDA-MB-231 and A549 division times are around 28 hours.
So I assume there is a physical barrier somewhere around one division per day or so, and it simply cannot grow faster. While bacterial division times are much lower (down to 20min), they also depend on special mechanisms (see this question/answer) and are orders of magnitude smaller than mammalian cells, so they don't count as a counter argument to this.
If you check zygote division times (10-12h, 14-16h, 22-24h, ...), you can see that they highly depend on the cell size. After some divisions the zygote depleted the reserves necessary to divide at higher rates, so after that it is limited by the ~24h barrier too.
Same 24h data here by rapidly proliferating cells.
So we can assume that 1/24h is the maximum rate of cell division by cancer. Let's read more about cancer in vivo, because it behaves completely different than immortalized cell lines in in vitro tests.
Originally tumours were thought to grow because they consisted of
cells that multiplied more rapidly than cells in the surrounding
tissue. In fact the average cell cycle of 48 hours for human tumour
cells is slightly longer than the cycle of non-malignant cells. ...
When a normal cell divides, it does os only to replace a cell that has
been lost and in this way a constant cell population is maintained. In
tumour cells the control mechanism appears to have been lost: as the
cell divides it adds to existing numbers of cells and increases the
total population. ...
A measure of the rate of tumour growth is the time taken for a given
population of malignant cells to double in size (doubling time). If
the cell cycle takes between 15 and 120 hours, the doubling time can
be between 96 hours and 500 days, depending on the histological type
of the tumour, its age and whether it is a primary or metastatic
growth. A shorter doubling time (less than 30 days) can be between is
seen with teratomas, non-Hodgkin's lymphomas, and acute leukaemias;
common solid tumours such as squamous cell carcinoma of the bronchus
and adenocarcinoma of the breast and bowel have doubling times in
excess of 70 days. In the patient the growth of a cacncer is only
detectable and observable during the last 10-14 of its 35-40 doubling
So according to this book the division rate of cancer cells are similar to healthy cells.
According to another book this statement is from Dougherty & Bailey 2001, but I wasn't able to find the scientific article. :S
Tumour cells appear to have lost control mechanisms which prevent cells from growing until replacement is required. Human tumour cells are thought to have an average cycle time of 48 hours. This is not more rapid than the cycle of most normal cells. The reason tumours become larger is because their cell division creates additional cells rather than replacements (Dougherty & Bailey 2001).