First, many historians would argue that the Six-Day War did not produce current attitudes in or about Israel, but rather that the war and current attitudes are the result of the war for independence in 1948 as well as dating back even farther to the Jews return to the region during the Old Testament time period.
During the Six-Day War, Israel prepared itself to stem off attacks from Jordan, Syria, and Egypt--countries who did not want Jews in the region. Before that time and still today, Israel has had to be prepared to be attacked by surrounding countries who did not want Jews occupying the area in 1948 and who do not want them occupying it now. While the Six-Day War focused on three specific countries' feelings about Israel, today the anti-Israel countries have merely changed. Nearby Iran's leader has promised to wipe Israel off the face of the earth; so Israel is in constant preparation for warding off an attack by Iran, even as it must address ongoing Palestinian conflicts.