"There's an agreement to get votes and I'm very happy about that," Sen. Susan Collins said.
Democrats linked the ruling to the GOP's "reckless refusal" to fill a Supreme Court vacancy.
Senate Democrats have dismissed the GOP agreement.
Democrats are pushing forward, vowing to keep holding the floor indefinitely.
Sarah Ferris 06/23/16 03:14 AM EDT
The House held a hurried vote around 3 a.m. Thursday.
Democrats launched a protest over inaction on gun control that lasted for more than 15 hours.
Sarah Ferris 06/23/16 12:49 AM EDT
The votes are expected early morning Thursday in the middle of a protest.
Pelosi and John Lewis's names appeared on fundraising emails mid-protest.
Armed with sleeping bags and pillows, Dems are vowing to carry on their protest.
Rep. Louie Gohmert shouted at Democrats who had taken over the floor.