In the wake of the exposure of two classified surveillance operations, most Americans expressed disapproval about the United States government’s collecting phone records of “ordinary” Americans. Yet, most showed little concern about their own Internet activities or phone calls’ being monitored.

A majority, 57 percent, said that the leaks about the surveillance programs would not affect the ability of the United States to prevent future terrorist attacks, while 30 percent said the fact that the programs had been made public would weaken the government’s efforts to prevent terrorism.

According to a CBS News poll released Tuesday evening, nearly 6 in 10 Americans said they disapproved of the federal government’s collecting phone records of ordinary Americans in order to reduce terrorism. However, three-quarters said they approved of the government’s tracking phone records of Americans suspected of terrorist activity. Nearly the same number approved of the United States’ monitoring the Internet activities of people living in foreign countries.

At the same time, a slim majority, 53 percent, said that collecting Americans’ phone records was a necessary tool to find terrorists, while 40 percent said it was not necessary.

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The poll found that almost 6 in 10 Americans are very or somewhat concerned about losing some of their privacy as a result of the federal government’s efforts to combat terrorism. However, 46 percent said the government had achieved the right balance between privacy and security concerns, while 36 percent said it had gone too far. Another 13 percent said the government had not gone far enough, with Republicans and independents more likely than Democrats to say the government had overreached.

A New York Times/CBS News poll conducted in April, after the Boston Marathon bombings, found a similar number of Americans saying the government had achieved the right balance between intrusion and privacy, but only 20 percent said it had gone too far, and 26 percent said it hadn’t gone far enough.

When it comes to their own communications being tracked, 6 in 10 Americans said they were not very or not at all concerned about the government’s collecting their phone records or monitoring their Internet use. Nearly 4 in 10 were somewhat or very concerned, and again, Republicans and independents expressed more concern than Democrats.

The CBS News poll of 1,015 adults on cellphones and landlines was conducted June 9-10 by live interviewers. It has a margin of sampling error of plus or minus three percentage points.