The Library of Congress may open its doors full time again. And then again, it may not.

Congress has to give final approval to -- and President Reagan must sign -- Sen. Robert Byrd's proposed $1 million appropriation authorizing extra funds for the library. Byrd (D-W.Va.) tacked the amendment on to the pending Senate supplemental appropriations bill, in order to restore some of the Gramm-Rudman-Hollings budget cuts that led to reduced hours for the library.

*The $1 million would come from surplus funds rescinded from the $49 million appropriated for the current renovation project on the Capitol's West Front. Byrd's proposal (currently under discussion before a House-Senate conference committee) would allocate $500,000 for the acquisition of new books, periodicals and newspapers; $160,000 for cataloguing services; and $340,000 for the library to stay open weekday evenings and Sundays.

At present the library is open Monday through Saturday from 9 a.m. to 5:30, with extended hours to 9 p.m. on Wednesdays. The proposed schedule would have the library open on its former schedule, weekdays from 8:30 a.m. to 9:30 p.m., Saturdays 8:30 to 5, and Sundays from 1 p.m to 5.

"We don't know what will happen," said library spokeswoman Nancy Bush yesterday.

"We can't do anything until the proposal is signed."