WASHINGTON — The Republican-led House is poised today to approve a bill that would give private sector workers the option of choosing paid time off instead of cash wages for working overtime.

The measure would allow employees who work more than 40 hours a week to save up their earned time off for use weeks or months later. GOP lawmakers say they want to give busy working parents at private firms the same flexibility that public sector workers have to take time off to spend with their children or care for aging parents.

Democrats and worker advocacy groups say it opens the door for employers to pressure workers not to take overtime pay. And they warn there is no guarantee workers would be able to take the extra time off when they want.

The bill is expected to pass today but has little chance in the Democratic-controlled Senate. President Barack Obama has threatened a veto, saying the bill would not prevent employers from slashing overtime hours and doesn’t offer enough protection for workers who may not want to receive compensatory time off in lieu of overtime pay.

The measure is part of a broader Republican agenda aimed at expanding the party’s political appeal by offering conservative ideas to help average Americans on issues like economic growth and job creation.