Am I hurting my chances if I delay my onsite interview by a week?

I was told today that the team wants to meet with me for an onsite interview and they asked for my availability. (they were vague, just said "let me know what days/times work for you"

This week at work I have a lot going on that I don't think I can get out of.. I asked if next week would be okay, but said that I could potentially make Thursday or Friday of this week work.

Do you think going in next week would hurt my chances? Like, if they are interviewing other candidates this week, I'm wondering if they're more likely to choose one of them..

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