Antonio Tajani spoke after listening to her address in Brussels, where she is meeting the other 27 European Union leaders on the talks, stalled over how to ensure a continued open Irish border after Britain leaves.
Talks on finalising the UK's withdrawal agreement and a political declaration on future trade relations with the EU have been blocked by failure to agree on a backstop to avoid a hard border between Northern Ireland and the Republic in the event that an agreement on future EU-UK relations can not be struck.
The US Trade Representative's office wrote to Congress yesterday to say it plans to start negotiations "as soon as it is ready" after Brexit Day on March 29, in news that will provide a welcome boost to Theresa May.
At present the two sides are proposing that Britain remain inside the European Union single market and bound by its rules from the time it leaves the bloc in March until December 2020, to give time for new trade relations to be set up.
"The problem is the Prime Minister", he said.
With the offer on the table, Europe is seeking to put pressure on May to come to Brussels with ideas of her own.
The choreography of Wednesday's summit opening emphasises British isolation.
The prime minister spoke for about 15 minutes at a dinner of all 28 European Union leaders, after which they will decide what their next move should be.
Senior EU diplomats said no new progress have been made.
Well, the issue here is all about sentiment and more specifically, deadlines.
But both London and Brussels have pledged to avoid any physical infrastructure, or "hard border", anxious that it could upset the delicate peace process that ended decades of violence between Protestant supporters of British rule over the province, and Irish Catholics nationalists, who believe in a united Ireland.
But Labour's Sir Keir Starmer said his party did not accept the choice facing Parliament was between "whatever deal Theresa May cobbles together or no-deal".
Back in Brussels, a stern Tusk said he had "no grounds for optimism" based on a report Tuesday from Barnier and May's appearance in parliament on Monday.
At the meeting in Brussels, EU leaders decided that not enough progress has been made in negotiations to warrant calling a one-off summit in November for a divorce deal to be signed.
The SNP's Stephen Gethins said it was clear the PM had "failed to bring forward any meaningful proposals to end the deadlock created by her Government".
The spokesman said: 'We want to secure a deal as quickly as possible.
Britain says it has not asked for an extension, but May has not yet come up with proposals for unblocking the Irish border logjam.
London believes frontier checks can be avoided through a new trade agreement with Brussels, but accepts the need for a fallback plan to address the issue until that deal is agreed.
But the idea is controversial among May's eurosceptic Conservative MPs, who fear it is simply a way of delaying Britain's exit.
UK Prime Minister Theresa May.
She also faces a rebellion from her parliamentary partners including the Northern Ireland's Democratic Unionist Party, who have said the proposal would tear Northern Ireland from the rest of Britain. She is hemmed in by pro-Brexit members of her Conservative Party, who oppose any more compromises with the bloc, and by her parliamentary allies in Northern Ireland's Democratic Unionist Party, who insist a solution can't include customs checks between Northern Ireland and the rest of the United Kingdom.
Also it is confirmation, if such were needed, of how hard it is for Barnier to drop a solution for Northern Ireland that introduces trade barriers with Great Britain.