The tense exchange occurred during a hearing on the status of the administration's reforms of the secret, bulk data collection program exposed last year by former National Security Agency contractor Edward Snowden.
Deputy Attorney General James Cole, testifying before the House Judiciary Committee, hesitated when asked whether the controversial NSA program that gathers the numbers, call times and lengths of virtually every US phone call extended to communications by members of Congress and executive branch officials.
"Without going specifically, probably we do, congressman," Cole said.
Issa then asked whether the president's phone calls were targeted by the program. Cole would not say, but agreed to get back to Issa with the information.
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Members of the panel warned the Obama administration to swiftly reform the NSA's bulk data collection program or risk losing overall authority to conduct such surveillance.
"If the bulk collection program was debated by the Congress... It never would have been approved," Sensenbrenner said.
The section of the law used to justify the program "sunsets" in June 2015, and with bipartisan congressional opposition to bulk data collection mounting, Sensenbrenner and others suggested it would not be re-authorized without a major overhaul.