From CBS News:
More than half of Americans — and an overwhelming number of Democrats — say they approve of the fact that Congress has opened an impeachment inquiry into President Trump. But as the inquiry begins, there is no national consensus on how to assess the president's actions.
Partisans have immediately and predictably split: most Democrats call the president's handling of matters with Ukraine illegal, and deserving of impeachment.
Most Republicans call his actions proper — or, even if improper, then still legal — and feel they're an example of things that past presidents typically did, too. Most Americans think that because Congress is now taking up the matter, it will be unable to work on other issues.
FiveThirtyEight on September 27:
Most early polls show uptick in support for impeachment
The final poll conducted in April, July and September* from pollsters that have released a poll after news about Trump’s call to the Ukrainian president first broke on Sept. 20
|SUPPORT FOR IMPEACHMENT IN POLLS TAKEN …|
|POLLSTER||POST-MUELLER REPORT (4/18)||POST-MUELLER TESTIMONY (7/24)||POST-UKRAINE NEWS (9/20)||OVERALL CHANGE|