The exchange, ahead of a summit of EU leaders to discuss Britain's departure, reveals the degree of acrimony stewing even before the two sides have formally sat down to haggle.
For the bloc, the key is to show a united front while May needs to increase her parliamentary majority, so she's not hostage to pressure from hardliners wanting a clean break or those seeking a softer landing.
Her ultimate goal remains to be seen.
May's itinerary shows the scale of her ambition to capture Labour-held districts. Leeds East has been held by Labour since the seat was created in 1955. It was represented for nearly 40 years by Denis Healey, one of the biggest names in the party since World War II.
For May, seeking to consolidate her grip on power, the timing is critical. While polls show her party with a 20-point lead against Labour, she has warned her Cabinet against complacency.
A YouGov survey yesterday showed that more British voters are regretting Brexit. Moreover, there is the real risk of voter fatigue setting in as many are put off by the prospect of a third vote in as many years.
A low turnout could harm May.
Conservatives are seeking to cast the June 8 election as a straight choice between her "strong, stable leadership" and a "coalition of chaos" led by the "weak and failing" Corbyn, the most unpopular Labour leader in at least 35 years and a frequent object of ridicule by the Tories.
Taking questions from the media following her speech, May didn't shy away from criticism of the Labour leader. She accused Corbyn of "failing to stand up for the defence of our country".
On tax, she said voters have a choice between the Conservative party, "which has been, which is and always will be a low-tax party", and a Labour party "whose leader has talked of putting up the basic rate of income tax".