Democrats' lead over Republicans on a generic House ballot was cut in half over the past month, according to a new American Barometer survey.

The poll, conducted by Hill.TV and the HarrisX polling company, found that 41 percent of respondents said they would vote for the Democratic candidate in their district, while 36 percent said they would go with the GOP candidate.

That compares with an American Barometer poll from August that showed Democrats had an 11-point lead: 45 percent said they would cast their vote for the Democratic candidate, while 34 percent favored the Republican candidate.

This month's American Barometer poll was conducted Sept. 8–9 among 1,000 registered voters. The sampling margin of error is 3.1 percentage points.

An average of polls from RealClearPolitics has Democrats leading Republicans by 8 points on the generic congressional ballot, while an NPR–Marist poll released on Wednesday shows Democrats with a 12-point advantage.

Robert Jones, the founder and CEO of the Public Religion Research Institute, told Hill.TV's Joe Concha on Wednesday that Democrats need to stay above 6 points in order to take back the House in November.

"As long as they stay above 5 1/2 points on average, that's where the tipping point is," Jones said on "What America's Thinking," which aired on Friday. "So if they stayed the same, about 6 points or more, that's a House flip."

Several political scientists have observed that due to the way Democratic voters are concentrated in urban areas, the party must have a sizable advantage in generic ballot polls in order to do well in federal elections.

— Julia Manchester