Among the challenges is stiff resistance from phone companies that do not want to be told how long to hold their customers' data if the government does not collect it, especially if that means longer than they do now, The Washington Post reported.
The companies do not have the data-sifting capabilities of the National Security Agency (NSA), which holds the records and uses them to sift for terrorist connections.
At one end is an odd mix of tea party Republicans and civil liberties Democrats who want the government to end its bulk collection of Americans' records, not just shift where the data are stored, it said.
At the other end are powerful lawmakers, including the chairmen of the House and Senate intelligence committees, who have resisted any substantial changes.
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Obama has tasked Attorney General Eric Holder and Director of National Intelligence James Clapper with devising a plan by March 28.
The official was referring to the pending expiration of Section 215 of the USA Patriot Act, the law that underpins the programme.
In some ways, the NSA controversy presents Obama with the inverse of the political problem he faced with the US military prison at Guantanamo Bay, Cuba, the report said.
The NSA harvests billions of records daily from phone companies about Americans' calls: the numbers dialed, and the lengths and times of calls. But the agency does not receive the call content. It stores the "metadata" for five years in an effort to map links to al-Qaeda and affiliates by running the numbers of suspected terrorists against the database.
In a speech last Friday, Obama said that this capability could be useful in a crisis.