The Conservatives flatly rejected claims on Tuesday that their proposals would open a £1.9bn black hole after their measures to boost employment through tax cuts had prompted a welter of conflicting claims over their effectiveness, simplicity and cost.

Underpinning the Tory plan is the belief that giving tax credits to companies taking on new staff will in effect pay for itself by creating jobs and cutting benefit payouts. The party argues such schemes have a proven record since they were pioneered by Jimmy Carter, the US president, in 1977.