This paper investigates the potential and economics of electrical space heating in Swedish single-family dwellings (SFDs) to provide Demand Response (DR) for the electricity load in Sweden. A dynamic and detailed building-stock model, is used to calculate the net energy demand by end-use of a set of sample buildings taken as representative of all Swedish SFDs with electrical heating. A new sub-model optimizes the dispatch of heating systems on an hourly basis, for each representative building, minimizing the cost of electricity purchased from the hourly spot market. The analysis of the Swedish SFD buildings indicates a technical DR capacity potential of 7.3 GW, which is considerable and can be used for the management of intermittent electricity generation. This potential could also prove to be valuable in the operating reserve market. However, this requires that the DR, rather than being governed by a single hourly electricity price signal, would instead be subject to a more centralized control. The modeling shows that DR can be expected to result in up to 5.5 GW of decreased load and 4.4 GW of increased load, if applying current Swedish electricity prices. The modeling shows that DR shifts up to 1.46 TWh of electric heating, corresponding to 1% of total Swedish electricity demand. The potential savings from DR for individual SFDs is found to be low, 0.9-330 €/year, given current Swedish electricity prices.