HILDY: All I know is that instead of two weeks in Atlantic City with my bridegroom, I spent two weeks in a coal mine with John Krupsky. You don't deny that, do you Walter?
WALTER: Deny it? I'm proud of it. We beat the whole country on that story.
HILDY: Well, I suppose we did. That isn't what I got married for!
Walter's ambition is unvarnished and unabashed; as long as he gets his story, he's proud. Hildy's more uncertain. She admits that they did a good job getting the story. But she's also concerned about personal things, not newspaper things. And really, who can blame her? If you can't put your ambition aside on your honeymoon, when can you? Walter's kind of a one-note jerk.
WALTER: That mayor would hang his grandmother to be reelected.
The mayor would hang his grandmother… but Walter would walk out on his own honeymoon to get a story. How different is the mayor than Walter, really? Walter does all sorts of crooked things in pursuit of his goal too. Maybe we're not supposed to like the mayor because he isn't played by Cary Grant?
WALTER: The movies will be after you. There'll be a Hildy cigar. I can see the billboards: "Light up with Hildy Johnson"
HILDY: Oh Walter, will you stop that acting? We've got a lot to do.
WALTER: Now you're talking.
Walter dazzles Hildy with images of her future success. Hildy has lots of ambition… but unlike Walter, she isn't quite in control of it. It gets the better of her. Walter just always puts his ambition first. As a woman, and as someone who is not a complete louse, Hildy doesn't, which means it can sneak up on her.
HILDY: This is the biggest thing in my life.
Hildy's referring to the story she's writing, and to her career. Bruce is upset to hear that she's putting her career ahead of him. Bruce is kind of a jerk (though, to be fair, he's had a rough day.)
HILDY: How you have messed up my life. What am I going to do?... I could be on that train right now. What a sap I am, falling for your line: "They're gonna name streets after me." Johnson Street!
"What a sap I am, falling for your line" sounds like it means she's fallen for a romantic line. Actually she fell for Walter telling her how famous she'd be. But the two things are constantly tangled together in His Girl Friday. Walter is Hildy's ambition personified; he's both the career and the guy who wants to marry her. It's hard to separate the two.