As West Virginia's elections chief, Secretary of State Natalie Tennant said her office could keep the tight timetable set out in either version if it wins final passage today.
"If they can get it passed tomorrow, we will be OK," Tennant said Sunday.
But that bill must also be written to take effect today. For now, only the Senate-passed version would do that. When the House approved the other version Saturday, supporters failed to muster the two-thirds majority needed for that effective date.
Without a bill, Manchin may still declare a special election, said Jim Pitrolo, his legislative liaison. Pitrolo cited the recent legal opinion from the state attorney general that concluded the governor had that power.
But Manchin might also do nothing, Pitrolo said Sunday.
The latter option would allow Manchin's temporary appointee to the seat, Carte Goodwin, to serve beyond November.
Manchin named Goodwin, his former chief counsel, on Friday under the premise that the 36-year-old would serve until a fall election. Goodwin is slated to be sworn in Tuesday.
Byrd died June 28 with slightly more than 30 months left in his term. The 92-year-old Democrat was history's longest-serving member of Congress, holding his Senate seat for more than a half-century.
Goodwin is a Democrat as is Manchin, who has said it's highly likely he would run for the seat if there is an election. Manchin's probable candidacy has played a role in the special session debate. So has the special election's estimated $5.9 million cost.
The attorney general's opinion, meanwhile, has prompted some lawmakers to question the need for the legislation. A related, party-line debate centers on whether Rep. Shelley Moore Capito, the GOP's top prospect if there is an election, can run both for Byrd's seat and a sixth U.S. House term on the same ballot.
The education bills passed Sunday by the Senate include one that would redraw some of the in-school decision-making or advisory committees. Another would require annual teacher evaluations. The remaining two would create pilot programs offering temporary pay boosts to educators and alternative settings for disruptive elementary and middle school students.