It is cheaper in the USA.....
But time off could be a problem. My mate did his in 2x 2week stints back in 2000 for this reason.
Looking a flights, in March you can get LHR to LAX return for £299.....
I'd have learned in the UK but for a) a 30 mile drive for each lesson, b) the cost, c) the length of time it'd take and d) the unpredictable weather. I did mine in 5 weeks, I could have completed in 4 but for fog the last week, and it was a great holiday which cost about $5000.....back in 2000 though.
Good luck!