In a survey conducted Oct. 3-6, 33 percent of those questioned named "dissatisfaction with government and elected representatives" as their biggest concern, the polling organization, based in Princeton, N.J., found.
Gallup said that was the highest percentage of disaffection with government recorded since it began its trend survey in 1939.
Concerts about the economy ranked second at 19 percent, followed by unemployment, the deficit and healthcare, all at 12 percent.
During the United States' last protracted shutdown in January 1996, 17 percent of those asked said a dysfunctional government was the country's top problem.
Last month, 16 percent of those polled said dysfunctional government was the country's biggest problem.
Concerns about the government were voiced more by Democrats (36 percent) and independents (33 percent) than Republicans (23 percent).
Syria, which was mentioned by 8 percent of respondents last month, was picked by only 1 percent of those polled this month.
Americans' approval of Congress is 11 percent, "within one percentage point of being the lowest in history," Gallup said -- noting that "trust and confidence in government was at record lows before the shutdown occurred, and the upheaval in Washington is causing Americans' confidence in the economy to drop precipitously."
Gallup polled 1,029 adults for the survey. The margin of error was calculated at 4 percentage points.