New Gallup data published Wednesday falls mostly into the second category. Gallup's Frank Newport and Andrew Dugan compared favorable ratings of the candidates in their daily surveys from the Saturday before the video release to results from Friday-Tuesday.
The poll found almost no change in Trump's overall favorable rating, from 32 percent before the video's release to 31 percent afterward. Clinton's rating also was stable over that period, 42 percent before Friday and 41 percent after.
Gallup's surveys did detect a five-point drop in Trump's favorable ratings among self-identified Republicans, from 69 percent to 64 percent. Newport and Duggan reported that Trump's image did not start to slump until Saturday interviews, "perhaps reflecting a delayed reaction to Republican leaders' public drop in support." Trump's favorable rating dropped to 61 percent among Republicans interviewed from Saturday onward, marking his lowest favorable rating in seven-day Gallup averages since June. His positive mark among Republicans is now far below Clinton's 84 percent favorable rating among fellow Democrats.
Besides Republicans, the poll found no shift in Trump's favorable rating among independents or Democrats -- in part because there wasn't much room to drop. Just 26 percent of independents had a favorable view of Trump both before and after the video, and a scant 5 percent of Democrats saw him positively at both points.
That stability comes despite widespread attention to the news. On Monday, 92 percent of Americans recalled reading, seeing or hearing something about Trump in the past day or two, and through the weekend "women" or "woman" were among the most frequently mentioned words in describing what they heard.
Gallup isn't alone in finding little shift in Trump's standing since the video was shown last Friday. An PRRI/Atlantic poll conducted Wednesday through Sunday found Clinton leading Trump by 11 percentage points in the overall vote choice, with a similar margin before and after the tape's release (12 points before, 11 points after). PRRI research director Daniel Cox cautions that the post-tape sample was more Republican and conservative than in the first days, which could explain why there was little movement.
Although the Gallup and PRRI polls show little impact of the video on Trump's popularity, they still show him in a weak position. His favorable rating in Gallup's survey is 10 points lower than Clinton's, and his 11-point vote choice deficit to Clinton in the PRRI/Atlantic poll is larger than her six-point edge one week before.
Still, some polls do suggest the video had an effect on Trump.
A national NBC News-Wall Street Journal poll conducted Saturday to Monday found Clinton leading by 9 points, a slightly wider advantage than her 6-point edge in the same poll in September and larger than that in most other surveys after the first debate.
State polls provide some more compelling evidence. This week, The Fix's Philip Bump explored a Marquette Law School poll that showed Clinton's Wisconsin lead expanding from one point on Thursday to six on Friday and 19 points on Saturday and Sunday of that survey. A Detroit News poll found Clinton up by 11 points in Michigan, slightly larger than her seven-point lead after the first debate. And in Utah, a Y2 Analytics poll immediately after the second debate showed Trump tied with Clinton at just 26 percent of the vote, about 10 points lower than his support in other polls in September.
The takeaway from the mix of results is that the video's publication had some negative initial effect on Trump -- but didn't prompt a big shift. The event may have solidified Clinton's growing lead after the first debate, which had already put her in a commanding position. The lack of major shifts in support makes sense for a long campaign in which Trump's support had already shrunk to a more loyal base below 40 percent of the electorate.
All these surveys represent the first look at Americans' reaction to the video and its aftermath. It will take more polls in the coming days to clarify the picture and also catch up with the other wild news of this week.