As someone who's bicycled and extended version of this in about a month without training using a loaded down mountain bike:
I can assure you that LA to Vegas on a road bike with a support vehicle is absolutely doable for anyone with a months worth of training.
My GPS data for proof:
21 June = 48 mi
22 June = 40.70 mi
23 June = 61.94 mi / 5157.4 ft
24 June = 34.41 mi / 1840.5 ft
25 June = Sick/Rest
26 June = 17.07 mi / 2749.3 ft
27 June = 58.62 mi / 5961.2 ft
28 June = 34.77 mi / 2070.2 ft
29 June = 39.51 mi / 1217.2 ft
30 June = 64.00 mi / 2831.3 ft
01 July = 32.15 mi / 4314.3 ft
02 July = 61.21 mi / 3914.0 ft
03 July = 40.30 mi / 1574.8 ft
04 July = Off
05 July = Off
06 July = 79.35 mi / 7975.6 ft
07 July = 35.40 mi / 4317.5 ft
08 July = 64.31 mi / 5049.2 ft
09 July = 57.63 mi / 5875.9 ft
10 July = 83.42 mi / 6240.1 ft
11 July = Off
12 July = 65.56 mi / 6223.7 ft
13 July = 26.88 mi / 2457.3 ft
14 July = 68.51 mi / 4071.5 ft
15 July = 75.09 mi / 3139.7 ft
16 July = 49.02 mi / 2086.6 ft
17 July = 75.57 mi / 4196.1 ft
18 July = 58.93 mi / 3116.8 ft
19 July = 36.60 mi / 981.0 ft
20 July = 75.86 mi / 3152.8 ft
21 July = 81.70 mi / 4055.1 ft
22 July = 90.09 mi / 4780.1 ft
23 July = 54.82 mi / 1473.1 ft
24 July = Off
25 July = Off
26 July = 74.50 mi / 5600.3 ft
27 July = 54.65 mi / 3848.4 ft
28 July = 38.11 mi / 3615.4 ft
29 July = 93.13 mi / 8028.1 ft
30 July = Off
31 July = Off
01 Aug = 21.37 mi / 2204.7 ft
02 Aug = 100.0 mi / 6538.6 ft
03 Aug = 17.54 mi / 1538.7 ft
04 Aug = 40.32 mi / 4078.0 ft
05 Aug = 77.25 mi / 5613.4 ft
06 Aug = 53.25 mi / 5196.8 ft
07 Aug = 28.17 mi / 1269.7 ft
08 Aug = 36.82 mi / 4954.0 ft
09 Aug = 89.92 mi / 6190.9 ft
10 Aug = 47.52 mi / 2824.8 ft
11 Aug = Off
12 Aug = 52.65 mi / 1863.5 ft
13 Aug = 115.39 mi / 3654.8 ft
14 Aug = 59.34 mi / 725.1 ft
15 Aug = 87.05 mi / 1522.3 ft
29 July = Almost 100 miles and 8000 feet of elevation. The last part of the day was 20 miles of uphill to 12,000 feet. You wanna talk about suck...
For a sack of gold coins, a stake in the WSOP, and a bunch of hookers ill make sure he wins this bet.