Legislation unveiled Tuesday that would make it easier for unions to woo workers to their cause could be the first real test of organized labor’s clout in the Democratic-controlled Congress.

Labor advocates, who played a major role in helping Democrats gain the House and Senate, have made what is termed “card-check” legislation a top lobbying priority.

Organized labor already claimed one partial victory when both chambers passed versions of a minimum wage increase (HR 2). But that measure — which now awaits conference — enjoyed broad bipartisan support, particularly after small-business tax breaks were added in the Senate.

The card-check bill is likely to have a much tougher path.

The measure (HR 800) was introduced by George Miller, D-Calif., who heads the House Education and Labor Committee. His Senate counterpart, Edward M. Kennedy, D-Mass., who chairs the Senate Health, Education, Labor and Pensions panel, said he will have companion legislation ready in the coming weeks.

Current law allows employers to insist on a second step, a vote by secret ballot after a majority of employees have signed cards, before a union can be certified as a bargaining agent.

Not all employers choose to have an election. Under Miller’s bill they would lose the option. It would do away with the second step, easing the path for organized labor.

Under the current system, once an election date is set, employers are free to campaign against the union, and many do so actively.

Labor groups, led by the AFL-CIO, say that gives management an opportunity to coerce workers to oppose the union.

“For too long, Congress has failed to act against the union-busting tactics now all too familiar in the workplace,” Kennedy said. “We have a new Democratic Congress now. It’s up to us to pass this important bill, and we intend to do it.”

Business groups say just the opposite is true: Doing away with elections would give labor organizers a chance to intimidate workers who would have no protection via a secret ballot.

“Such mandatory card checks can strip workers of the right to choose — freely and privately — whether to unionize,” said Howard P. “Buck” McKeon of California, the ranking Republican on the Education and Labor Committee, “and card checks notoriously leave workers open to coercion, pressure and outright intimidation and threats.”

Miller has scheduled a hearing Thursday on the measure in the Subcommittee on Health, Employment, Labor and Pensions. He did not say when the legislation would be marked up.

In addition to changing the certification process, the measure would take steps to push employers and unions toward agreement on an initial contract and create penalties for intimidation of employees.

The bill would give the employer and the union the option of moving toward mediation on the first contract if they cannot agree within 90 days. If mediation fails to produce a result after 30 days, the parties would go to arbitration, with the results binding for two years.

Under current law, the sides have a duty to bargain in good faith but are under no obligation to reach an agreement.

The bill would give the National Labor Relations Board the authority to seek a federal court injunction against employers when there is “reasonable cause” to believe that the employer has discharged or discriminated against employees, threatened to discharge or discriminate against employees or has engaged in conduct that “significantly interferes” with the employees rights while organizing.

The bill would also institute civil fines of up to $20,000 against employers found to have “willfully or repeatedly” violated employees’ rights while organizing.