WASHINGTON — The Republicans’ first test of their new Senate clout could come in a vote to block President Barack Obama’s choice of a union attorney for a seat on the National Labor Relations Board.

Senate Democrats need 60 votes, one more than they control since Scott Brown of Massachusetts was sworn into office last week, to clear a GOP procedural hurdle to advance Craig Becker to a final Senate confirmation vote. That procedural vote had been scheduled for Monday but was postponed until today because of a Mid-Atlantic snowstorm over the weekend.

Democrats’ task turned more difficult when Sen. Ben Nelson, a conservative Nebraska Democrat, said Monday night he would join Republicans in opposing Becker.

“Mr. Becker’s previous statements strongly indicate that he would take an aggressive personal agenda to the NLRB, and that he would pursue a personal agenda there, rather than that of the administration,” Nelson said in a statement.

“This is of great concern, considering that the board’s main responsibility is to resolve labor disputes with an even and impartial hand. In addition, the nominee’s statements fly in the face of Nebraska’s Right to Work laws, which have been credited in part with our excellent business climate that has attracted employers and many good jobs to Nebraska,” Nelson said.

Republicans have held up Becker’s confirmation for months, saying they fear he will push an aggressive union agenda at the agency that referees labor disputes between unions and management.

The scuffle over Becker is part of a more heated conflict between business groups and unions over the Employee Free Choice Act or “card check” bill that would deny companies the right to demand an employee representation election before they have to recognize a union as a collective bargaining agent.

Becker, a lawyer for the AFL-CIO and the Service Employees International Union, has spoken favorably on card check. Some of his legal writings suggest that its goals could be accomplished by the NLRB without Congress having to pass the legislation.

Those writings alarmed the U.S. Chamber of Commerce, which poured more than $1 million into television ads supporting Brown during the chaotic closing campaign days before Massachusetts’ special election last month to fill the Senate seat of the late Edward M. Kennedy. The chamber is also allied with groups that launched an online petition urging Democratic leaders to postpone any votes until after Brown’s swearing in.

Chamber executive vice president Bruce Josten called Becker’s views “well outside the mainstream.”

Becker and his supporters attempted last week to play down the writings as scholarly ruminations.

“I don’t have any illusions that those important changes can somehow be accomplished administratively and neither does Craig Becker,” said Iowa Sen. Tom Harkin, chairman of the Senate Health, Education, Labor and Pensions committee.

For unions, Brown’s surprise win in Massachusetts has been a frustrating setback.

“Republicans stalled Becker’s nomination for five months and now accuse Democrats of trying to rush him through,” said AFL-CIO legislative director Bill Samuel.

The tussle over Becker is also another setback for the NLRB, which has been waiting for more than two years with vacancies in three of its five seats. That has forced the agency to postpone hundreds of cases that could have a wider effect on the workplace.