Housekeeping genes are genes that are continuously transcribed. Like all other genes they have promoter sequences, but they don't have TATA box sequences that are used to specify from where transcription is going to begin.
Why don't housekeeping genes have a TATA Box in their promoter sequences?
Two possible answers:
First, TATA boxes has been found to cause increased "noise" in gene expression, such that the expression of genes that have a TATA box is highly variable. See this review for example.
A different set of results suggests (here) that TATA acts only as an amplifier of expression.
Regardless of whether TATA amplifies expression or also increases expression variance, this is not suited for housekeeping genes, which generally have low and constant expression.
The TATA-box element (and notion of house-keeping genes) are classical textbook examples of trying to explain complex biology in a simplified manner.
In fact, most mammalian genes do not have a TATA-box element and most transcription start sites (TSSs) are spread over a larger area in the 5' end of the gene. Each TSSs contributing to differences in gene expression strength and gene product. This phenomenon has been extensively investigated using cap analysis of gene expression (CAGE). For a short summary of the major findings you can refer to Rikens website here.
Sandelin and Carninci et al wrote an excellent review on the findings of the first CAGE experiments here, and how this contradicts classic textbook promoter structures Nature.
In addition, the CAGE technology, has been used to map out cell-type specific enhancers which contribute hugely to the correct gene regulation, Anderson et al. Nature.
I know this answer does not directly address your question, but rather raises a lot of new questions.
Quick googling located online version of Lodish et al Molecular Cell Biology. 4th edition.
From TATA Box, Initiators, and CpG Islands Function as Promoters in Eukaryotic DNA section:
These genes, which generally are transcribed at low rates (e.g., genes encoding the enzymes of intermediary metabolism, often called “housekeeping genes”), do not contain a TATA box or an initiator
Also, from Transcriptional Regulatory Sequences of the Housekeeping Gene for Human Triosephosphate Isomerase (Boyer et al, J Bio Chem 1989):
In contrast to facultative gene promoters, these promoters are characterized by [...] and, notably, the lack of an appropriately positioned TATA box [...] Based upon these structural differences, the possibility exists that initiation of housekeeping and facultative gene transcription proceeds through distinct mechanisms.
I can imagine you can google more information, but it seems to me that reason for lack of TATA is necessity for constant low-level expression (hence no strong promoter) and separate mechanism of regulation (hence some common structure). Last point might arise from redundancy argument: when regulation of TATA-containing genes become faulty, housekeeping genes regulation stays same because it is somewhat independent.
However, you should be aware that your original assumption is at least controversial (from same J Bio Chem paper):
Unlike most housekeeping gene promoters that have been described to date, the human TPI promoter harbors a canonical TATA element (5’ TATATAA 3’) that spans positions -27 to -21. LS mutagenesis demonstrated that this TATA box clearly represents a control element, the integrity of which is essential for the maintenance of both the fidelity and the frequency of TPI gene transcription initiation.
