WASHINGTON — As a crucial series of gun-control votes approaches in the Senate, lawmakers on Capitol Hill are suddenly preoccupied with one question in particular: when is Frank Lautenberg coming back?

Mr. Lautenberg, a New Jersey Democrat and the oldest member of the Senate at 89, has been out for weeks dealing with health complications partly from cancer treatment he received several years ago.

But with Democrats scrambling to come up with enough votes to overcome resistance to the most sweeping gun-control legislation in a generation, Mr. Lautenberg’s presence (or absence) is shaping up to be critically important.

Aides insist that Mr. Lautenberg, who has been undergoing physical therapy for weeks, will try to get to Washington once the voting begins on the assortment of gun-safety measures, which are expected to come to the floor in the coming weeks.