We examine the question of how glassiness can remain finite in the van der Waals model of structural glass in situations where the Ginzburg criterion near the spinodal line of fluid instability against crystallization is satisfied. For d < 4, d being the dimensionality of space, finite glassiness demands certain conditions for the long-range interaction potential. For 4 < d < 6, no such condition is required, whereas for d > 6, the Ginzburg criterion becomes irrelevant. We comment on the relationship between dynamic and static calculations of the nonergodicity parameter.