WASHINGTON — Democrats were adjusting grudgingly to their reduced role in the Senate on Wednesday, displaying some surliness and a lot of suspicion while making the case that they would not be silent or passive players in the new Republican-controlled Congress.

In so quickly assuming the role of the aggressors on only the second day of the session, Democrats struck a discordant tone when compared with Republican pleas for greater bipartisan cooperation.

Resistance came from the West Wing as well. On Wednesday morning, the White House issued President Obama’s second veto threat in 24 hours by pledging not to sign a Republican bill that would redefine a full-time worker under the Affordable Care Act. The administration on Tuesday said that it also would veto legislation authorizing construction of the Keystone XL oil pipeline, another Republican priority.

Senator Harry Reid of Nevada, the Democratic leader, at home recovering from broken bones sustained in a workout accident, dispatched his deputy, Senator Richard J. Durbin of Illinois, to read a defiant statement from the Senate floor.