WASHINGTON — As the government shutdown dragged on, Senator Susan Collins of Maine was spending another weekend on Capitol Hill, staring at C-Span on her Senate office television as one colleague after another came to the floor to rail about the shuttered government.

Frustrated with the lack of progress, Ms. Collins, a Republican, two Saturdays ago quickly zipped out a three-point plan that she thought both parties could live with, marched to the Senate floor and dared her colleagues to come up with something better. A few days later, two other Republican female senators eagerly signed on — Lisa Murkowski of Alaska, who overcame the Tea Party to win re-election in 2010, and Kelly Ayotte of New Hampshire, who benefited from the Tea Party wave.

Together the three women started a bipartisan group whose negotiating framework formed the centerpiece of a tentative Senate deal nearing completion Monday to reopen the federal government and avert a disastrous default.

“Before I went to the Senate floor, no one was presenting any way out,” Ms. Collins said. “I think what our group did was pave the way, and I’m really happy about that.”