Yes we can!
This today according to the AP:
In late-stage talks, Obama and Senate Majority Leader Harry Reid, D-Nev., pressed for $8 billion to construct high-speed rail lines, quadrupling the amount in the bill that passed the Senate on Tuesday.
Reid’s office issued a statement noting that a proposed Los Angeles-to-Las Vegas rail might get a big chunk of the money.
As someone who lives in Los Angeles County, my family and I would use it.
In other words, if they built it, we would come.
The current drive between the two cities is atrocious and mind-numbingly long—and frequently dangerous and backed-up with traffic.
And one can imagine a great deal of economic growth along the route of the railway, especially if there was a stop or two in-between.
Prometheus Unbound 
An excellent idea considering California , Nevada , and Arizona economies are inter twined to a significant degree. Can you imagine the fuel costs that will be saved. Also can you imagine Las Vegan’s working in Los Angeles and vice versa? The potential money saving benefits are astronomical not to mention the dramatic decrease in carbon emissions which will help mitigate the acceleration of climate change. This type of infrastructure project should have been launched decades ago and I’m very thankful we’re finally taking the first steps to catch up with our European brothers and sisters.
It looks like Los Angeles to Las Vegas is a bit shorter than Paris to Lyons apparently one of the busier routes in the French system. You do need new track although you could use existing right of ways and the last time I looked it is about US$25 million/km (a handy figure for us metric types) and the cost would be about US$10 Billion or less than one month of the wars in Iraq and Afghanistan.
(posted to save somebody else from looking this trivia up.)