WASHINGTON — The last whimpers of the gun control debate in the Senate played out in anticlimactic fashion on Thursday as lawmakers began the process of formally moving on.

All that remained of a broad package of measures representing the most serious changes to the nation’s gun laws in 20 years were two amendments: one that would address mental health care, and another that would penalize states that divulge information about gun owners except under very specific circumstances like a criminal investigation.

Both passed overwhelmingly, the only two gun-related measures to clear the Senate’s 60-vote threshold for passage. The vote on the amendments has no practical effect, since the underlying legislation has no immediate prospect of passing.

Despite the push from proponents of stricter gun regulations, the amendments that received the most support in two days of voting were not the ones that tightened restrictions on weapons purchases, but the ones that loosened them.