Some Archaeologists, particularly those who belong to the so called Minimalist school, have denied for years that the kings David and Solomon ever existed or ever reigned over a significant territory. The arguments between them and their opponents depend on highly technical issues, such as how to date layers of earth in which certain objects were found (stratigraphy), as well as how to date events in the Tanakh. However, it generally boils down to the question of whether Israel was had a significant monarchy in the 10th century BCE, which is deduced from the size of the remains of building of that period. Kings need forts, garrisons, industries, stabes, etc. Since, so argue the Minimalists, little evidence was found of any extensive buildings of that period, there were probably none.
The arguments cannot be considered in a vacuum, one also needs to understand the cultural baggage that individual archaeologists bring, as well as their personal biases and those of the respective institutions they work for. Those who are fascinated by biblical archaeology know what I am talking about.
Interestingly, recently several finds have come to light that do close some gaps in our knowledge and now, some archaeologist admit that there plausibly could have been an Israelite monarchy at that time. (You wouldn’t expect too many of them to say that there actually was such a monarchy – let’s take it slowly ;-))
See the following recent articles:
This comes on the heels of an older report that King David’s palace may finally have been found: King David’s Palace Is Found, Archaeologist Says (New York Times, 2005; including obligatory remarks to sound even handed, OY what nonsense can find its way into respectable papers in order to stay Politically Correct ™)