In the previous post, I mentioned that the Wills et al (2008) analysis did not include any cladogram that included both dinosaurs and birds.
But the Pol and Norell (2006) study did:
Uncertainty in the Age of Fossils and the Stratigraphic Fit to Phylogenies
It included the theropod taxa. That study found that the theropod option produced an MSM* of 0.31 to 0.40.
This appears to be the best, most objective info we have about a theropod to bird cladogram being compared to the fossil record. The fit is exceptionally low.
It shows that the dinosaur-to-bird theory is not congruent with the actual fossil record.