Yes to the first part but maybe no to the second.
They thought that holding the two by-elections last month would somehow draw a line under events and move on, yet here we are a few weeks later and similar problems are arising. It’s impossible for him to now shake off the image that he’s presiding over some kind of bacchanalian orgy while the rest of the country is on its uppers.
It’s also one thing to see the Liberal Democrats overturn big majorities in by-elections, but were Labour to take Tamworth, it would be an even greater concern: it would propel Starmer forward as a serious challenger. For that reason, I presume they’ll try desperately hard not to have another by-election