Tom Donilon - who spent three years as the most senior voice on foreign policy in the Obama administration - was clear. On issues where America dealt directly with the EU, issues like the nuclear deal with Iran, immigration and aid spending, not being present at the EU table would lessen Britain's importance for the US.
But Mr Donilon's overriding concern was not one of specific foreign policy issues it was a broader question of focus. Voting leave, he fears, would lead to a Britain that is more inward looking and more distracted from global affairs.
That, he added, would be a less powerful partner for the US. On a string of critical issues, Britain would be less important to the White House if it were not part of the European Union.
I sat down with Mr Donilon, President Barack Obama's previous National Security Adviser, after he and a group of senior American foreign policy officials signed an open letter urging Brits to vote to stay in the EU on June 23rd. He acknowledged that it was unusual for American officials, from the president down, to weigh in on a British political issue. However Mr Donilon felt the stakes are so high for Britain, the EU and the US that it was important to do so.

Communities Secretary Carl Sargeant said last month he was not convinced Communities First was the "most effective way to deliver for Wales".
He said there would be a new approach but, so far, community groups supported by the scheme say they are in the dark.
The Welsh Government said no final decision had been made.
In Swansea, Faith in Families, which runs three family centres, said it would be forced to close without Welsh Government support.
It is converting St Teilo's Church in Swansea into a Â£1m community hub with half the money provided by the Welsh Government.
Boss Cherrie Bija said: "We are not going to give up on these families."
She added that people were "really disappointed" after hearing the phasing out of Communities First would have a knock-on effect on the services the centre could deliver.
Communities First spends about Â£30m each year, with more than Â£300m spent since it was launched in 2001 and, at one point, it was supporting about 200 projects.
In Flintshire, Dave Wisinger, the county councillor for Queensferry, said the Communities First office covering his area provided crucial support.
"There has to be something else to take over," he said.
"And I would have thought the minister, if he has a serious look at this, he will appreciate the good work that's been done and he will keep these staff on, or as many as they can...maybe under another project."
Communities First supports four dementia cafes in Flintshire, helping those with the condition and their families, as well as running food banks, lunch clubs and family learning sessions.
It also runs job search clubs and employability courses.
Mother-of-two Kelly Latham from Garden City, who attended once such course in Mold, said: "I've been unemployed for nearly five years now.... child care's a big issue for me... and they've sorted it all out for me."
A Welsh Government spokesman said: "Although the communities secretary has said he is minded to phase out Communities First, no final decision has been made.
"We are currently seeking views on this and how to engage, support and strengthen communities and would urge anybody with an interest to have their say.
"It is too early to speculate on how any new approach might impact on particular areas."
How would the relationship between the White House and the UK change if Britain were no longer part of the EU?
[NEXT_CONCEPT]
Community groups are seeking assurances following the announcement that a scheme which supports deprived areas in Wales is set to be dropped.