This question has been posed in many different ways. Your best bet is to read these threads under Money and Legal tab of this web site. The short answer - unfortunately - is usually no. That said, there are a very few programs - the VA & some states that might pay you to stay home with a relative. There are very specific criteria to meet. Contact your local state dept of health and welfare office to see if your state offers care giver stipends. Your nearest Veterans Affairs office can help you understand the criteria to qualify, if your father qualifies for VA benefits.
Remember that, you can declare your father a dependent and reduce your taxes if you provide more than 50% of his annual financial support - be sure to consider all room and board, clothing, food, electric, etc. This won't help you on a monthly basis, unless you're spouse is working and can reduce the amount of tax paid each month. Before doing this, talk with an accountant or tax preparer to understand what's involved.
Remember that, you can declare your father a dependent and reduce your taxes if you provide more than 50% of his annual financial support - be sure to consider all room and board, clothing, food, electric, etc. This won't help you on a monthly basis, unless you're spouse is working and can reduce the amount of tax paid each month. Before doing this, talk with an accountant or tax preparer to understand what's involved.