You can check out the calculated molecular orbitals of water on Professor Zipse’s (LMU Munich) page. The surrounding ‘text’ in German need not interest you, just click on mo-number to access an image of the corresponding MO.
The lowest orbital with the lowest energy is, of course, oxygen’s core $\mathrm{1s}$-orbital. Next up we have an all-bonding orbital deriving from oxygen’s $\mathrm{2s}$, an all-bonding deriving from oxygen’s $\mathrm{2p}_x$ and a predominantly bonding one deriving from oxygen’s $\mathrm{2p}_z$. You could combine these three to give an almost $\mathrm{sp^2}$ type environment around oxygen with two $\mathrm{sp^2}$ orbitals involved in bonding to hydrogens and the third being an oxygen lone pair. (However note that $\mathrm{sp^2}$ is typically associated with $120^\circ$ while water has a bond angle of $105^\circ$.)
The final orbital is $\mathrm{2p}_y$ according to the way I defined the coordinates (diagram below). This is essentially π type with respect to the $\ce{O-H}$ bonds, so it is nonbonding (hydrogen cannot bond in a π manner). This represents the second lone pair of oxygen.
The two ‘lone pairs’ (remember that by an MO description all orbitals are delocalised across the entire molecule) are notably different from each other, that includes their energies. So calling them equivalent in an $\mathrm{sp^3}$ manner is wrong. $\mathrm{sp^2}$ is a description that would fit the calculated energies, but not so well with the geometry.
