It shouldn't. I have had many clients who obtained their green cards despite bad credit. It does, however, sometimes make it more difficult for a married couple to combine their assets as evidence of a bona fide marriage.
*The information provided here is for educational purposes only and should not be relied upon without first consulting with an experienced immigration law attorney. This information should not be relied upon as legal advice and is not intended to create an attorney-client relationship.
USCIS doesn't typically check credit scores, but if you are in the I-130/I-485 stage, then you do have to prove that you can sponsor or support the immigrant. If this is questionable, and you have a qualifying (age, relationship, status, income) relative, you can have a joint sponsor, and if your immigrant spouse has assets and employment, that can be submitted as supporting documentation. After the first marriage interview, and prior to approval of the lifting of the conditions of the residency, it may or may not come up again about the financial situation changing. Assets can also be used to reach requirements of a shortfall of income as well... but so far, in my practice experience, "bad" credit or "credit scores" have not been a subject of inquiry to a beneficiary or the petitioner. You should carefully review the I-864 form for the ins and outs of what you ARE legally responsible for and what the qualifications are if you have not read or reviewed this, the Affidavit of Support (which is part of the first marriage filing in a typical case).