(CNN) The Senate on Tuesday passed and will send to the White House a broad defense policy bill that would block the President from bringing terrorism suspects held in Guantanamo Bay, Cuba, to the United States.

Unknown is whether President Barack Obama -- who made closing the detention center a key campaign promise -- will veto the bill or sign it despite the Gitmo restrictions.

The overwhelming and bipartisan vote was 91 to 3, which means it has more than enough supporters to override a presidential veto, though Obama's Press Secretary Josh Earnest said the President would sign the defense bill.

"A number of provisions in the NDAA that are important to running and protecting the country," Earnest said during a White House briefing, adding "that certainly does not reflect a change in our position, or intensity of position, of the need to close the Guantanamo Bay prison."

Congressional Republicans are bracing this week for what they fear will be a decision by the President to cite his executive authority and order the prison closed.

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