Is your husband in the US? If he is then you have to file an I485, in which case you have to provide an Affidavit of Support, so your unemployment may affect your petition. If your husband is not in the US then you don't have to provide an Affidavit of Support right not but you will have to eventually. I would recommend you consult with an Immigration Attorney to get a full comprehensive review of your case.
All comments and/or opinions are for general information, and should not be used as legal advice. In addition any comments and/or opinions do not create an attorney-client relationship. In order to obtain a comprehensive and accurate legal opinion you should consult an attorney with the specific and detailed facts or your case/question.
If you are going to sponsor your spouse for lawful permanent resident status through an I-130 petition, you will have to show that you are able to support him. There are ways to prove your ability to support even if you have been and are unemployed by having someone "co-sponsor" or by taking into account your and your prospective husband's assets. Please consult an experienced immigration attorney so that you don't make an expensive mistake.
Your unemployment will not affect whether our Form I-130, Petition for Alien Relative is approved. It will be an issue that needs to be dealt with regarding his eligibility to either adjust status, if he is present in the U.S., or receive an immigrant visa to enter the U.S. As my colleagues have stated you as the petitioner become the sponsor for purposes of the Form I-864 Affidavit of Support. If you are unable to show a sufficient income or combination of incomes and assets, you can use a joint sponsor to help meet this support requirement. it is best to have this issue resolved before it becomes a problem. You should consult with an experienced immigration attorney to determine what you will need to do.
Unemployment will not affect your I-130 petition. It could, however, affect your husband's application for his green card. There is a mandatory requirement to show that he will have financial support to avoid becoming a public charge.
This answer is of a general nature and does not in any way create an attorney-client relationship.