Elena Baltacha and Anne Keothavong both lost their opening rubbers, meaning they must win all three of Sunday's matches to win the tie.
Baltacha lost the first match 6-1 7-5 to Johanna Larsson before Keothavong went down 6-1 6-4 to Sofia Arvidsson, at 54th in the world the highest-ranked player in the tie.
British number one Baltacha will look to at least avoid a whitewash when she plays Arvidsson on Sunday before Keothavong is slated to play Larsson.
Should a deciding tie be required, Heather Watson and Laura Robson will play Arvidsson and Larsson in a doubles rubber.
