There are ample examples of a municipality taking private property so it can be sold to a private company which will result in a higher tax base. Just look to the US Supreme Court decision in Kelo vs. New London {New London wanted to seize a bunch of homes so a developer could build a campus for Pfizer - court said that the states get to decide what "public purpose" means and upheld the right}
Based on the Kelo decision, it would be likely that this concept could be considered "public", but it is a stretch even with the broad Kelo ruling. These mortgages being targeted are current and the homeowner is making the proper payments -- I do not see how it can be argued that people who are currently making their mortgage payments are creating a "blight" that hurts the public. If they were going after loans that were past due and ready for foreclosure, that would be different - since foreclosure and vacant homes hurt everyone around them {personally, I still do not feel this is correct - but apparently the court did not take my feelings into account}
Another problem is that to use Eminent Domain, the governemtn is forced to pay fair market value for the thing taken -- in the example in the article of the $300K mortgage, I do not know that they can claim $120K is the fair market value. I am not knowledgable in valuing notes, but I understand the value of the property that the lien attaches to is just one aspect of the valuation -- credit of borrower, payment history, etc. all factor in.
What I think will sink this idea is that the city is not the one pressing this issue, it is a venture capital company. The argument will be that the venture capital company is looking to acquire good value notes at discount prices (which is why they are going after the notes where the borrower can actually pay) and are simply going to give a kickback to the city based on the profit.
Also, I think if one note gets seized, I can see every bank in CA banding together to fund the defense regardless of how small the mortgage holder is -- this is potentially billions of dollars of loss to the banks, they will throw millions of dollars at making sure it does not happen and I bet the venture capital group that is pressing this is not going to fund the city's defense.