According to a new GAO (Government Accountability Office) report, the Department of Homeland Security only has "operational control" of 44% of the U.S.-Mexico border, and only 15% of the border is "controlled" (the highest level that GAO measured). A write-up is here and the PDF is at this link.

On the plus side, the percentage under operational control has been rising over the past five years (see the chart in the PDF). And, in some cases (such as around Big Bend in Texas) the terrain might make crossing much more difficult and thus much less likely than around San Diego. Note also that the definitions of whether an area is secure doesn't necessarily mean that someone wouldn't be able to cross the border, just that they'd eventually be caught in that region:

Border Patrol’s definition of operational control considers the extent to which its agents can detect and apprehend illegal entries, but does not require agents to have the ability to detect and apprehend all illegal entries, according to officials in Border Patrol’s Strategic Planning and Policy Analysis Division. Yuma sector, for example, reported operational control for all of its border miles although Border Patrol did not have the ability to detect and apprehend illegal entries who use ultra-light aircraft and tunnels.8 In fiscal year 2009 Yuma sector reported that of the known illegal entries, about half were apprehended somewhere in the sector, about 40 percent were turned back across the border sometime after entry, and about 10 percent were "got aways."

Nearly two-thirds of the 1,120 southwest border miles that had not yet achieved operational control were reported at the “monitored” level, meaning that across these miles, the probability of detecting illegal cross-border activity was high; however, the ability to respond was defined by accessibility to the area or availability of resources (see fig. 5). The remaining miles were reported at “low-level monitored,” meaning that resources or infrastructure inhibited detection or interdiction of cross-border illegal activity. Border Patrol reported that these two levels of control were not acceptable for border security.