Looks like the Senate Democrats will focus on Alito's participation in the Vanguard case. David McGowan blogged extensively on this below. I want to see what shakes out, but for now I expect this will turn out to be a minor oversight that had no effect on how the case turned out. To recap some of the main issues being raised in Alito's defense: Vanguard was simply holding money that two parties were fighting over; it's virtually impossible that Alito's ruling could have had any impact on the value of his holdings; it's hard to believe (impossible to believe?) that Alito ruled on the case with the specific intent of siding with his mutual fund company; and his vote had no impact on the outcome.
Another, larger issue is the extent to which computer searching for conflicts results in lawyers and judges relying more and more on the computer "hits" rather than on racking their brains to spot conflicts. I can't say that's what happened here, but it's quite possible. My guess is that the affair will eventually focus on human memory, computer data, and inadvertence.