Working backwards from this carbon calculator's result of 203 pounds of CO2 per Southwest traveller between LAX and SFO (Southwest chosen due to being the most commonly cited and advertised airline between the two airports and their entirely economy seated aircraft), we can see a fuel consumption of 9.6 gallons per passenger per flight with $24-29 per ticket being devoted simply to paying the fuel cost (depending on 2010 hedged SWA price vs current market price). The portion of the price paid simply to account for the fuel costs is quite large, as much as half the ticket price with current $59 discounted fare sales but still remaining a solid 25-30% of the ticket fare at the more common $99 fare level that travel on that route sees this year (for an advance purchase ticket).
This rise in fuel prices is not indefinitely sustainable of course. Too high of an oil price will cause major drops in consumer spending as increased transportation costs raise the price of goods and lower household discretionary incomes. At a certain breaking point, this causes a sufficiently large drop in demand as to cause an economic downturn, reducing the price of oil. Until and unless significant forces of alternative fuels (be it Fischer-Fropsch synthetic fuel, biofuel, or widespread adoption of electric cars and mass transit) or a coordinated price fixing action by the oil producing nations act to stabilize the price of oil, this will result in a perpetual cycle around the "sustainable" price.
Still, it is certainly possible for oil to increase sustainably by another 50% (to an average world price of $150 dollars per barrel and an airline price of $4.50 per gallon) or catastrophically double (to $200 and $6 respectively). This would push up the fuel price between LAX and SFO to $43.20 and $57.6. If airline operating expenses and profit seeking (in terms of dollars per ticket) remain fixed and fares only rise in accordance with fuel, our $99 baseline fare would rise to $114 and $129. Assuming that other factors similarly rising (such as wages to deal with transportation expense inflation) meant that fuel did not exceed 40% of the total airfare, only the catastrophic scenario would see a price rise, to $144 per ticket.
While this would impact transportation to a degree, in neither case does it seem that air travel between the Los Angeles and San Francisco regions would be greatly affected. There is a sufficiently high degree of travel that increased fuel costs are unlikely to so greatly reduce demand and profit margins such as to significantly reduce service.
Among the trains cited in "Estimating Emissions from Railway Traffic" (page 74), the TGV Atlantique, which runs 300 km/hr maximum and 240 km/hr average between Paris and St. Pierre des Corps (Tours), best represents CAHSRA's planned 350km/hr top speed, 220km/hr average speed train between Los Angeles and San Francisco. That train consumes 22 kilowatt-hours per kilometer for a total consumption upon the 695 kilometer route of 15,290 kilowatt-hours. With 485 seats, if we assume an average train capacity factor of only 50%, the energy consumption will be 63 kilowatts per passenger. At the 2010 price of electricity for transportation customers in California of 8.46 cents per kilowatt-hour, the fuel price per passenger is a mere $5.32.
This does not mean, of course, that high speed rail tickets will necessarily be able to drastically undercut the price of airlines. Rail, after all, has significant infrastructure maintenance costs that airlines do not. Renfe financial report shows traction energy costs amounted to only 7.5% of total expenditures (source, page 163). Following that result, if averaging only 50% of total seat capacity, a break-even fare, of all operational costs, would be $71, declining to $50 at 70% capacity factor. Electricity is somewhat cheaper in Spain, but this should not greatly affect matters. SNCF reports energy costs averaging 4.3% of total costs from amongst all divisions, with the result of much higher train fares if that were to hold true for CAHSR ($123).
In the end result, higher oil prices are not likely to impose a significant burden to air demand although competitive pressure may lead to failures and consolidations before ticket prices rise to match fuel costs. Provided that gold-plated design can be avoided, maintenance costs kept low, and tendencies towards overstaffing as currently demonstrated by American passenger rail kept at bay, the California high speed rail system stands a very good chance of potentially greatly undercutting airline fares and establishing itself as the major low cost carrier of high speed intrastate intercity travel.