It depends on what the "Background Check" is. If it's just an HR formality, then I'd either insist on a guarantee of a certain amount of pay (6 or 12 months) IN WRITING, or tell them to just wait it out. They're probably using a clearing house that takes a while, and don't want to pay an expedite fee. These are really annoying, as there's very little assurance that the agency will "get it right" and it's just a thing they have for marketing, like cleaning services have.
If it's for a financial sector, or perhaps even a full SSBI security check, those can take weeks and/or months, because they are thorough. Companies that play in the "Major leagues" with these know what they are doing. They have a great deal of onboarding and training that you'll have to go through, and they also have non-secure work to do while waiting for these to complete. These are the "Big boys," and would not have even extended you an offer if you hadn't passed an initial background check (which they can do very quickly).
If this is Raytheon, then they know what they're doing and I'd proceed. If this is "Ray and Leon's Software Consulting," I wouldn't jump until they make a firm, unconditional offer.
My opinion only, your mileage may vary.