Normalcy? Not on the republican side; there was nothing normal about that party since Gingrich turned the system on it's head as
Speaker of the House (short Wikipedia summary).
I think that the probability will be high that negotiations on bills with bipartisan interest will result in passage - with both sides yielding on some points. Then the spin doctors will go to work, simultaneously giving victory to the republican senators and decrying the bill for the socialist agenda clearly being pushed even further on the democrats side. Fox news will create 'sensational' videos which will then show up on the rest of the MSM channels and social media. So that bullshit will go on, possibly for decades to come.