What does it mean exactly? (...she'll be big with health care after she has...)

[Kwfine]

I was listening to my local radio station, and heard of a man asking an interviewee with this question:
"...do you think she'll be big with health care after she has become the CEO..."
I have looked it up into an online dictionary,
and it has this example sentence: "be big with a child" meaning pregnant.
But the example actually makes me feel so confused even more than ever...

Could someone help explain what the interviewer asked in the radio please?

[Jamie (K)]

The question meant, "Do you think she'll be an enthusiastic supporter of healthcare after she has become CEO?"