In Diamond's model, Romney's tax rate changes effect the economy primarily in two ways. Most importantly the lower marginal tax rate leads individuals to work more hours each year, and both enter the work force earlier and work longer into old age. Diamond models the tax rate cut as a reduction in marginal wage tax rates from 26% to 20.8%, which results in an aggregate increase in labor supply of almost 6%. He then uses results from a different paper (Blundell Bozio Laroque 2011) to argue that 90% of this increase would be from additional workers joining the labor force. That gives him the 7 million new jobs number. Reading Blundell et al is key to understanding what is wrong in Diamond, and why this is nonsense.

Blundell tries to explain the labor supply response to changes in the effective wage rate (which is what is left after taxes). They find that these changes are extremely heterogeneous across different workers. In particular they find that women with children, very young workers and those on the verge of retirement are quite sensitive to wage rates, and tend to either work or not - this response is called elasticity of extensive labor supply. Almost all the change in labor supply in response to wage changes comes from these segments choosing to enter (or remain in) the labor market.

Diamond's paper has representative agents - everyone is identical in wealth and earning power except for differences that result from their age, so the women entering the workforce is not in his model (no women, no marriage, no children). He should be able to capture young and old workforce entry, but doesn't do that because the effect is negligible in his model. That is why he uses the Blundell result to estimate the number of jobs - his model has no jobs created.

But the Blundell model is not consistent with the base model of the paper. Diamond's model is about the labor supply response to the tax change. Blundell shows that the response is almost nothing for most workers, but very strong for a few subgroups. Diamond's result depends entirely on a response which Blundell finds is negligible.