There is no visa in the US that allows the bearer to work remotely for a foreign employer. If you're planning to stay in the US as a "visitor for business or pleasure" for longer than 90 days, you would need a B visa (B-1 or B-1/B-2 as a business visitor; B-2 or B-1/B-2 as a "pleasure" visitor).
As a B-2 visitor, you are allowed to undertake incidental tasks related to your employment, such as e-mail, telephone calls, and so on. As a business visitor, you can also attend meetings, negotiate contracts, and other similar activity. There's no clear guidance concerning full-on working, but anecdotally it seems that if you apply for a visa saying that you intend to be working full time, remotely, for your foreign employer, the visa will be refused. Similarly, if the immigration officer discovers the same intention, you will not be admitted to the US.
This may not make much sense, especially in terms of fostering the US tourism sector, but that seems to be how it works these days.
For what it is worth, Canada has explicitly taken the opposite position on this question, so you might consider going there instead.
Another thing to keep in mind is that your pay for the work you perform in the United States is likely taxable in the United States.