Ms Pelosi, whose party controls the House, said the UK’s exit from the EU could not be allowed to endanger the Irish peace deal.
Her comments came after the US national security adviser said the UK would be “first in line” for a trade deal after October 31 – the Tories deadline for Brexit.
John Bolton spoke after meeting Prime Minister Boris Johnson in London.
Said Mr Eastwood: “Today’s intervention from the Speaker of the US House of Representatives Nancy Pelosi marks Boris Johnson’s cards.
“The fantasy trade deal that Brexiteers like Johnson and Farage have been salivating over will not happen if they continue on their path to a hard Brexit and a hard border in Ireland.
“I welcome Nancy Pelosi’s strong and consistent commitment to the letter and spirit of the Good Friday Agreement.
“Her identification of a seamless border as a key test of Brexit is now a critical objective if the new British Prime Minister wants to land what he obviously sees as his big Brexit prize.
“A seamless border and a no-deal Brexit are mutually exclusive objectives. Boris Johnson’s administration now has to recalculate its strategy and return to the cold reality that the backstop is the only show in town.”