The response time for new projects is anywhere from 2-6 years (or more) depending on the complexity of the project (a simple tie-back to an existing platform, versus a major new development in an area with little infrastructure). So there's been time for a response to show up.

The EIA appears to believe that US oil production would have at least some elasticity (they show substantially different production profiles based on price). Of course Exxon is only one data point, but as either the largest or second largest of the oil majors, and a highly diversified one, they are exposed to a significant cross-section of the industry, so that the fact that they cannot (or won't) increase production is significant. Most of the other majors are actually in decline:

The main exception, BP, has primarily been benefiting from significant exposure to a Russian subsidiary.

I should add that their annual reports generally show an intent to increase production. Eg. spot checking Exxon's 2001 and 2004 reports, in 2001 they intended to grow production by around 3% annually, and in 2004 they intended to grow at about 3 1/2% a year to 2007. However, it doesn't seem to pan out that way.

Here's their exploration spending from the 2004 annual report. Doesn't look like we should expect a fundamental change in the next few years.

I'd love to see this an Excel 'Area'-type chart with 100% area including these OIC numbers as a percentage of the total liquids daily production for the same period.