If you ask them if they like their job, this may put them on the spot and make things awkward. But it also may actually only be awkward if they hate their job. If they love their job, they'll likely burst right into a story of why it's so great and tell you some stories that also gets you excited about the role. If it gets awkward, that may be a red flag, and it may be a sign you'll want to look for other forms of discontent in the organization.
But you should go deeper than just this one question. As Joel Etherton suggests, you could start by asking what the interviewer likes most about his or her job. Taking this to a deeper level, you could ask what it was like for them when they first started the job. Ask how easy it was to learn the ropes and get information to be effective in that person's new role. Ask what the company did to make that person feel welcome when they first came on board.
What you're looking for is to gauge the interviewers reaction to these questions. If they seem hesitant, or pause, or look like their head is hurting when trying to answer the question, this may mean there's a problem that this person doesn't want to expose. It may not mean it's a bad place to work, but if you get that same "I have an excedrin migraine" look from enough people, it may indicate there is something majorly wrong in the corporate culture.
If you ask questions about someone's experience, like "How well do people in the office get along with each other?" and the interviewer lights up and tells stories that reaffirm this statement or even tells stories of conflicts that end with those same people going to get lunch together afterwards, then this is a good sign. It's a sign the organization is more likely to be built on mutual respect and be filled with problem solvers.
I'm not going to list every possible question you could ask, as that isn't what our site is about, but use the interview as a possibility to ask genuine questions about the work and culture, and then look for cues that there's a feeling of helplessness in the organization or hesitation to answer questions.
Aside from the interview, if you don't get interviewed by the team, consider trying to contact an employee to ask them some basic questions. When I interviewed for my current job, I called the sales and customer service lines and talked to the people who answered the phones. I told them who I was and what I was doing, and they happily answered my questions. They were very positive people, and assuming this represented the typical person at the company, I felt confident that accepting the offer would be a good decision.