Moments later, the Senate approved an amended version by voice vote, a move that should allow the House to vote to conference with the Senate on the bill Thursday.

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The language in the Senate bill related to new import sanctions against Iran and rebels in the Congo, which affect tariffs and government revenue. The House and Senate agreed to tweak that language in a way that avoids the hurdle, although few details were available beyond that as of Wednesday evening.

The House has tried to vote to conference with the Senate on the NDAA all week, but now should be in a position to do so Thursday. The House-passed NDAA is H.R. 4310.

The Senate also agreed to name conferees to the bill, something the House might do as early as Thursday. The Senate conferees are:

Carl LevinCarl Milton LevinThe Hill's Morning Report - Biden officials brace for worst despite vaccine data Michigan GOP unveils dozens of election overhaul bills after 2020 loss How President Biden can hit a home run MORE (D-Mich.), Joseph Lieberman (I-Conn.), Jack ReedJack ReedOvernight Defense: US fires 30 warning shots at Iranian boats | Kabul attack heightens fears of Afghan women's fates | Democratic Party leaders push Biden on rejoining Iran deal Overnight Defense: Former Navy secretary reportedly spent .4M on travel | Ex-Pentagon chief Miller to testify on Jan. 6 Capitol attack | Austin to deliver West Point commencement speech Overnight Defense: Gillibrand makes new push for military sexual assault reform | US troops begin leaving Afghanistan | Biden budget delay pushes back annual defense policy bill MORE (D-R.I.), Daniel Akaka (D-Hawaii), Ben Nelson (D-Neb.), Jim Webb (D-Va.), Claire McCaskillClaire Conner McCaskillDemings asked about Senate run after sparring with Jordan on police funding Republicans fret over divisive candidates Greitens Senate bid creates headache for GOP MORE (D-Mo.), Kirsten GillibrandKirsten GillibrandAustin tight lipped on whether to take sexual assault cases out of commanders' hands Gillibrand touts legislation to lower drug costs: This idea 'is deeply bipartisan' A bipartisan effort to prevent the scourge of sexual assault in the armed forces MORE (D-N.Y.), Mark UdallMark Emery UdallKennedy apologizes for calling Haaland a 'whack job' OVERNIGHT ENERGY: Haaland courts moderates during tense confirmation hearing | GOP's Westerman looks to take on Democrats on climate change | White House urges passage of House public lands package Udalls: Haaland criticism motivated 'by something other than her record' MORE (D-Colo.), Richard Blumenthal (D-Conn.), Kay HaganKay Ruthven HaganBiden's gun control push poses danger for midterms The two women who could 'cancel' Trump 10 under-the-radar races to watch in November MORE (D-N.C.), Mark BegichMark Peter BegichAlaska Senate race sees cash surge in final stretch Alaska group backing independent candidate appears linked to Democrats Sullivan wins Alaska Senate GOP primary MORE (D-Alaska), Joe ManchinJoe ManchinManchin, Biden huddle amid talk of breaking up T package Biden to go one-on-one with Manchin There will be no new immigration law under Biden, unless he changes course MORE (D-W.Va.), Jeanne ShaheenCynthia (Jeanne) Jeanne ShaheenKabul attack spurs fears over fate of Afghan women as US exits Bowser on Manchin's DC statehood stance: He's 'not right' If Taliban regains power, they would roll back rights for women: US intelligence MORE (D-N.H.), John McCainJohn Sidney McCainEx-McSally aide pleads guilty to stealing over 0K in campaign funds DOJ: Arizona recount could violate civil rights laws Cheney fight stokes cries of GOP double standard for women MORE (R-Ariz.), Roger WickerRoger Frederick WickerThis week: Congressional leaders to meet with Biden amid GOP reckoning Biden to meet with GOP senators amid infrastructure push Biden visits local Mexican restaurant to highlight relief program MORE (R-Miss.), Scott Brown (R-Mass.), James InhofeJames (Jim) Mountain InhofeOVERNIGHT ENERGY: Senate nixes Trump rule limiting methane regulation | Senate confirms EPA chief: Biden's climate goals are 'an opportunity to lead' | Fine-particle pollution disproportionately hurts people of color: research EPA chief: Biden's climate goals are 'an opportunity to lead' Senate confirms Pentagon policy chief criticized by Republicans for tweets MORE (R-Okla.), Saxby ChamblissClarence (Saxby) Saxby ChamblissEffective and profitable climate solutions are within the nation's farms and forests Live coverage: Georgia Senate runoffs Trump, Biden face new head-to-head contest in Georgia MORE (R-Ga.), Susan CollinsSusan Margaret CollinsTop female GOP senator compares Cheney ousting to 'cancel culture' Utah county GOP censures Romney over Trump impeachment vote House conservatives take aim at Schumer-led bipartisan China bill MORE (R-Maine), Jeff SessionsJefferson (Jeff) Beauregard SessionsOne quick asylum fix: How Garland can help domestic violence survivors Biden fills immigration court with Trump hires Trump admin got phone records of WaPo reporters covering Russia probe: report MORE (R-Ala.), Rob PortmanRobert (Rob) Jones PortmanHouse conservatives take aim at Schumer-led bipartisan China bill Strengthen CBP regulations to reduce opioid deaths House panel advances bipartisan retirement savings bill MORE (R-Ohio), Kelly AyotteKelly Ann AyotteSununu seen as top recruit in GOP bid to reclaim Senate Lobbying world Overnight Defense: NATO expanding troops in Iraq MORE (R-N.H.), Lindsey GrahamLindsey Olin GrahamHouse conservatives take aim at Schumer-led bipartisan China bill There will be no new immigration law under Biden, unless he changes course McConnell safe in power, despite Trump's wrath MORE (R-S.C.), John CornynJohn CornynThere will be no new immigration law under Biden, unless he changes course Tim Scott sparks buzz in crowded field of White House hopefuls Cornyn is most prolific tweeter in Congress so far in 2021 MORE (R-Texas) and David VitterDavid Bruce VitterBiden inaugural committee to refund former senator's donation due to foreign agent status Bottom line Lysol, Charmin keep new consumer brand group lobbyist busy during pandemic MORE (R-La.).

— Jeremy Herb and Ramsey Cox contributed