Lawmakers awaiting a deal on how to avert a series of tax increases and spending cuts set to take effect early next month are biding their time by sorting out some issues at the nation’s airports.

The House gave final passage Wednesday to the No-Hassle Flying Act, a bill allowing the Transportation Security Administration to use more discretion in screening checked baggage arriving in the United States from certain international airports. Currently passengers arriving from countries with TSA-approved screening procedures don’t need to go through a security checkpoint after completing the customs pro­cess.

But checked baggage often must be rescreened by the TSA, a scenario that causes many passengers to miss connecting domestic flights, deterring international tourists from visiting the United States and delaying military troops returning from overseas deployment, according to co-sponsor Sen. Amy Klobuchar (D-Minn.).

Klobuchar admitted that her bill might not have passed so easily if there wasn’t a need to fill the time before a fiscal deal is reached: “I figure when you have a lull in action, use it to your advantage,” she said.

Also concerning the nation’s airports, senators unanimously approved a bill Tuesday night requiring the TSA to turn over thousands of items of clothing left behind at security checkpoints to homeless military veterans by partnering with local homeless shelters or veterans groups. The bill recently cleared the House, but must be passed there again because senators tweaked the bill’s language.

Sen. John D. Rockefeller IV (D-W.Va.) called the measure “a small but significant opportunity” to help the nation’s homeless veterans. The Department of Veterans Affairs announced Monday that it counted 633,782 homeless veterans on American streets this year, a 7.2 percent decline from 2011.

With the clock ticking toward the end of both the year and the 112th Congress, the airport bills are among several modest measures passed in recent days as the House and Senate eagerly await an opportunity to vote on the legislative branch’s marquee agenda item: a plan to avert the “fiscal cliff,” a series of tax increases and spending cuts set to take effect in January.

On Wednesday the House also gave final approval to a bill requiring the Department of Homeland Security to pass a full financial audit in 2013. Lawmakers have long sought an extensive review of the department’s finances as government watchdogs warn that DHS entities remain vulnerable to waste, fraud and abuse.

Despite the bills poised to pass this week, several other issues remain unresolved. Senate Majority Leader Harry M. Reid (D-Nev.) said this week that his non-fiscal-cliff to-do list includes striking a deal with the House on the annual defense authorization bill, a renewal of the Foreign Intelligence Surveillance Act, and approval of a $60 billion supplemental spending request from the White House to aid New York and New Jersey communities affected by Hurricane Sandy.

House Speaker John A. Boehner (R-Ohio) said Wednesday that he expects his chamber to also consider the supplemental request, but fiscally conservative Republicans have signaled they want to slash federal spending by a similar amount in order to pay for storm aid.

The Obama administration and House Republicans are also in talks about a deal on reauthorizing the Violence Against Women Act. Aides said that Vice President Biden and House Majority Leader Eric Cantor (R-Va.) have met to discuss disagreements involving jurisdiction of tribal courts over non-Indian domestic abuse claims, extending the law’s protections to homosexual couples and possibly expanding the number of visas available to immigrants who cooperate with law enforcement in some prosecutions.

Rosalind S. Helderman contributed to this report.