The Obama administration is in the final stages of drafting a plan to shutter the Guantanamo Bay prison facility in Cuba, White House press secretary Josh Earnest told reporters Wednesday.

Sen. John McCain, R-Ariz., has been openly discussing his talks with the White House about giving him a plan to close the prison that he could try to sell to fellow Republicans in Congress.

But this is the first admission by the White House that they are working on such a plan, despite repeated questions about it from the Washington Examiner and other media outlets.

The administration is "in the final stages of drafting a plan to safely and responsibly close the prison at Guantanamo Bay," Earnest told reporters Wednesday.

"That has been something that the national security officials have been working on for quite some time," he said.

In order to reduce the current prison population of 116 inmates further, Earnest said the administration wants to "responsibly transfer" detainees that Defense Secretary Ash Carter has certified do not pose a threat to U.S. security to foreign countries, and will continue to do so.

In the strongest terms to date, Earnest also said Obama would veto a defense spending bill now under consideration in Congress that includes language imposing new restrictions on detainee transfers and making it harder to close the prison. Obama, however, has not carried through on veto threats of the defense spending bill in the past.

A spokesman for House Speaker John Boehner, R-Ohio, said most Americans don't want the prison to close.

"The American people — and bipartisan majorities of Congress — have long opposed closing Guantanamo Bay and bringing dangerous terrorists to U.S. soil," Cory Fritz said. "Given the serious threats America faces, it's incredible to see this administration threatening to veto a bill that gives our troops a pay raise, strengthens our cybersecurity and imposes greater restrictions on releasing terrorists."