The only modern US warship I can find that didn't go radically over budget is the Virginia-class, and that's probably because they're a low-cost Seawolf.
Virginia-class: 4% under budget for Block II, on budget for Block I
LCS:63% over budget (Assuming follow-up units don't follow in the footsteps of the lead unit in the Independence class, that is. Which seems like it may actually work out.)
Ford-class:30.5%, using initial cost estimates of $8 billion/per unit, adjusted for inflation, and excluding research and development costs.
Zumwalt-class: 183% overrun, excluding R&D.
So pardon me if I'm just a little skeptical that another new ship class would stay even remotely within budgetary constraints, given recent history.