Should the White House nominate members through normal channels, he added, "I will pledge to work with the chairman for their speedy confirmation."
In January, the court ruled that Obama's made the appointments during a period in 2012 when the Senate was not technically in recess. The chamber was holding brief, pro-forma sessions every few days.
The Obama administration has since appealed the case to the Supreme Court.
Currently, the board, which protects union activity and worker rights, has two vacancies in addition to the two disputed members. If those two were removed, it would have just one member, short of the three necessary to take formal action.
In February, Obama renominated the two NLRB members whose appointments the court had found unconstitutional, and in April he renominated Gaston Pearce and submitted two new members to the Senate, Harry Johnson and Philip Miscimarra.
"If I could have chosen I would have preferred my potential service on the board to have come at a when the agency was not enmeshed in profound constitutional and political disagreements," said Johnson said. "But here we are, and here I am, because I said yes."
In reaction to the federal court ruling, Republicans in the House voted in April to freeze all of the board's current work and block all of its current enforcement actions. Senate Republicans have pressed a similar measure and repeated their calls for the members to resign on Thursday.
Liberal members on the panel complained of a pattern of Republican opposition, pointing to struggles of nominees to lead the Environmental Protection Agency, Department of Labor and Consumer Financial Protection Bureau.
Many Republicans "are actively trying to shut the NLRB down," said Tom HarkinTom HarkinGrassley challenger no stranger to defying odds Clinton ally stands between Sanders and chairmanship dream Do candidates care about our health or just how much it costs? MORE (D-Iowa), the committee's chairman.
"This is about complete obstructionism because a minority of senators don't like the agencies and they don't like the work these agencies do," Sen. Elizabeth WarrenElizabeth WarrenHow the candidates for DNC chair stack up ahead of Saturday's vote DeVos: 'My job isn’t to win a popularity contest with the media' Protesters crash McConnell's speech MORE (D-Mass.) added.
Sen. Bernie SandersBernie SandersMichael Moore touts Ellison for DNC: ‘We need fresh blood’ Tommy Chong: Trump pot crackdown 'will be defeated in court' DNC chair campaigns scramble ahead of tight vote MORE (I-Vt.) pushed Democrats to deploy the so-called "nuclear option" of altering Senate rules to prevent a filibuster of the nominees.
"If once again this effort is obstructed, if the goal is to prevent the NLRB from functioning in terms of protecting the rights of American workers, I think we should change the rules and take a majority vote to not only see that these people are seated so that they can do their job, but that other nominees who have been clearly obstructed should also have a chance to do their job," he told the committee.
The panel will vote Wednesday morning to send the package of nominees to the full Senate.