Are Dems in the house as lockstep as those in the Senate?

Short answer is no.

They have some work to do to bring the far left closer to the center if they want to be taken seriously in the next election cycle.

If they attempt to legislate from the far-left, they will get crushed.

I just saw an interview with Conner Lamb ( PA) and he said flatly:

Will not vote for Pelosi as speaker
Is interested in infrastructure and lower Rx
Not interested in Trump tax returns
No evidence for impeachment and thinks it’s silly to talk impeachment

He seemed genuinely to be “moderate”. We will see if it survives the infection of DC.