You may be liable for tax in the UK on rental income (I am not certain of the precise rules these days), but the US rules for taxing rental income are dramatically different from those in the UK and there are numerous deductions that you make from gross rental income to reach net taxable income, such that if you have a valuable property and a significant mortgage you can quite possibly have a taxable loss for the purposes of calculating your US tax liability. Deductions include the following: mortgage interest, depreciation of the building (but not the land - use 80% of the purchase price as a rule of thumb for the cost of the building unless you have good reason to use a different split, such as if the land has significant development potential) at a rate of 1/40 per year, insurance, agent/ management fees, interest, repairs and maintenance, marketing and advertising, property taxes (if any), etc.

Obviously if you have a valuable home then depreciation can be quite a large sum - a £500,000 home, including £100,000 for the land, would generate £10,000 of depreciation, and a £200,000 mortgage might generate an interest charge of another £10,000, and those two alone would wipe out most of £2,000/mth rent.

Note deducting depreciation is mandatory.