WASHINGTON — California Rep. Hilda L. Solis won bipartisan Senate support Friday for her nomination to be Labor Secretary in the Obama administration. But the battle lines were clearly — if politely — drawn for a potential clash on legislation that is a top priority of unions.

“Your life is one that epitomizes the American dream,” said Sen. Michael B. Enzi of Wyoming, the ranking Republican on the Health, Education, Labor and Pensions Committee, which held a hearing on whether to recommend full Senate confirmation — seemingly a foregone conclusion soon after President-elect Barack Obama takes office. Solis, 51, is the daughter of immigrants, the first in her family to attend college (on a Pell grant), and a veteran public official who has served eight years in the House

But Solis resisted repeated Republican efforts to pin her down on whether she and Obama will seek early action on the “Employee Free Choice Act,” a bill that would make it easier for unions to organize workers into collective bargaining units. It would have workers indicate a desire to join a union by filling out a card, rather than voting by secret ballot — hence the bill’s nickname, “card check.” Business is staunchly opposed to the measure.

Solis reaffirmed Obama’s support for the bill but said she couldn’t talk about the administration’s plans for it because she has not discussed it with Obama. She similarly deflected questions about other controversial labor issues.

Without committing themselves to any legislative timetables, Democratic senators, including Edward M. Kennedy of Massachusetts, the panel’s chairman, and Jack Reed of Rhode Island made the case that unions are an important instrument for improving American wages and working conditions.

Obama faces a dilemma on the legislation. He supported it as a senator and he owes a debt to organized labor, which worked hard and spent heavily to elect him. But Obama also campaigned on a promise to end the bitter partisan divide in Washington in order to make the government work better. Few actions would irritate Republicans and their business constituency more than an early campaign to push the unionizing measure into the law books.

“It would set the tone for the whole Congress,” Enzi said, “and I don’t think it will be a good tone.”

Republican Sen. Lamar Alexander described his efforts as a onetime governor to encourage the non-union Japanese automaker Nissan to build a factory in his state of Tennessee — and the unionized General Motors to locate a plant nearby. Solis declined Alexander’s request to say whether she would protect current law that permits workers to refuse to join unions in Tennessee and 21 other “right-to-work” states.

Reed said the wages of Tennessee’s non-union Nissan workers “wouldn’t be as high if there wasn’t a union” in the nearby GM plant.