The latter question offers the court a narrower way to rule on recess appointments.
Verrilli seemed to signal he would rather lose on that question than the first two. But under any circumstance he said, "You really are writing the recess appointments power out of the Constitution," he said.
The importance of recess appointments has dimmed in recent months, since majority Democrats changed the Senate's rules to make it harder for the minority party to block the president's nominees to federal agencies and the courts.
But the issue could once again be front and center when the White House and Senate are controlled by different parties.
Senate Republicans' refusal to allow votes for nominees to the NLRB and the new Consumer Financial Protection Bureau led Obama to make the temporary, or recess, appointments in January 2012.
Three federal appeals courts have said Obama overstepped his authority because the Senate was not in recess when he acted. The Supreme Court case involves a dispute between a Washington state bottling company and a local Teamsters union in which the NLRB sided with the union. The U.S. Circuit Court of Appeals for the District of Columbia overturned the board's ruling, and hundreds more NLRB rulings could be voided if the Supreme Court upholds the appeals court decision.
Three federal appeals courts have upheld recess appointments in previous administrations.
Washington lawyer Miguel Estrada represented Senate Republicans on Monday. Estrada withdrew his appeals court nomination in 2003, after Senate Democrats used the rules that recently were changed to repeatedly prevent a vote on the Senate floor.
With seemingly no trace of irony in his voice, Estrada said the Constitution erected a political structure that requires the branches of government to cooperate. "You have to act jointly. You have to play nice," he said. "And in a country of 300 million people, it's always possible for the president to come up with another nominee who is even more qualified and acceptable to the Senate."
A decision is expected by late June.
The case is National Labor Relations Board v. Noel Canning, 12-1281.
Associated Press writer Sam Hananel contributed to this report.