Attorney general nominee Loretta Lynch at her confirmation hearing in January. (Kevin Lamarque/Reuters)

Senate leaders agreed Tuesday to clear a legislative clog that has delayed the confirmation of President Obama’s attorney general nominee for more than six weeks and distracted attention from bipartisan efforts to pass major policy measures in the early months of a Congress newly under Republican control.

Loretta Lynch, a U.S. attorney in New York, is expected to win confirmation as soon as Thursday under the deal, which ended a partisan dispute over abortion restrictions in an unrelated bill. Senate GOP leaders insisted on clearing that impasse before moving forward with Lynch.

The agreement prompted Republicans, starting with Senate Majority Leader Mitch McConnell (R-Ky.), to boast about Congress “getting back to work” after a narrowly averted shutdown of the Department of Homeland Security presented doubts earlier in the year.

“There’s some encouraging signs that lots of people are noticing,” McConnell told reporters Tuesday.

Later in the day, the Senate began voting on amendments to long-stalled legislation to combat human trafficking, with final approval expected Wednesday. That would clear the Senate to vote on Lynch and then move on in the coming weeks to several bills that have passed in committee votes with at least some bipartisan support.

They include legislation establishing a congressional review of any final deal with Iran over its nuclear program, something that was initially strongly opposed by Obama but that ended up clearing the Senate Foreign Relations Committee on a unanimous vote. Also waiting in the wings are major bills to enhance national cybersecurity efforts, to reauthorize federal education programs and to grant presidential “fast track” authority to negotiate trade deals.

Members of the House and Senate budget committees are now hashing out a final spending plan whose passage will allow both houses to begin the process of taking up appropriations bills — which become vehicles for policy proposals that might not otherwise make it into law.

The early accomplishments have come at a glacial pace, and the process has, at times, looked much like the brinkmanship of recent years. Still, there are signs of potential progress, particularly on issues where Republicans have been able to meld strong support within their own party with significant Democratic support.

The biggest feat has been on a long-term “doc fix,” a bill making changes to the rates Medicare pays doctors. Obama signed it into law this week after the Senate approved a deal forged in the House between Speaker John A. Boehner (R-Ohio) and Minority Leader Nancy Pelosi (D-Calif.).

Another example of the modest but notable gains came Tuesday when Congress sent to the White House an energy-efficiency bill, drafted by Sens. Jeanne Shaheen (D-N.H.) and Rob Portman (R-Ohio), that had broad bipartisan support in the previous Congress but became a political football ahead of the November midterm elections.

The senators reintroduced the bill, and, in an after-midnight vote, it passed the Senate in late March with no opposition. The House gave its approval by acclamation Tuesday.

The Medicare legislation, meanwhile, succeeded out of a bipartisan willingness to tackle a pesky yearly ritual of rate readjustments and the willingness of most Republicans to look past a significant budget impact. The anti-trafficking bill and the Lynch nomination, to many observers, should have moved much more swiftly but became entangled in partisan battles over abortion and immigration, respectively.

But if McConnell can keep the forward momentum, he can claim to have made good on his pledge to lead a “responsible, right-of-center governing majority,” as he put it in a December interview with The Washington Post.

The recent movement looks even better considering the historically dismal baseline from which the current Congress is working: With the parties at near-constant loggerheads, the two most recent Congresses passed fewer bills than any other in the past four decades.

Senate Democrats say that the recent thaw is evidence that their mind-set as a minority is different from GOP behavior in previous Congresses. Where, in their telling, McConnell was focused on blocking most any Democratic initiative as minority leader, their objective is to stall and stall some more until Republicans give enough ground to forge compromise.

“Here’s the bottom line: I’m willing to stand up and see legislation pass, because I want to make sure that we’re a constructive minority,” Minority Whip Richard J. Durbin (D-Ill.) said Tuesday.

But being constructive holds political risks for Democrats, with Republicans eager to tout their governing prowess and with some issues — trade and government surveillance, most notably — exposing deep rifts within their own conference. That had several Democrats this week playing down claims of a new day on Capitol Hill.

“Let’s be honest — what do we have to show for the first three and a half months?” Durbin asked. “Four weeks on a human trafficking bill that should have been resolved quickly? I don’t think there’s a lot to show.”

Democrats filibustered the ­anti-trafficking bill after it came to the Senate floor in late February, because of abortion restrictions embedded within it, and McConnell vowed not to move forward with Lynch’s confirmation until the trafficking bill was cleared.

The deadlock was broken after both parties agreed on language specifying that a victims fund established by the legislation would not be used for medical services, and thus not for abortions. Trafficking victims would instead be eligible for health care under a separate program already subject to the long-standing abortion restrictions known as the Hyde Amendment, which contains exceptions for cases of rape and incest.

Senate GOP aides insisted that McConnell felt no pressure to strike a deal, given most Republicans’ opposition to her confirmation. But there was a palpable sense of relief Tuesday that the standoff had eased.

“We needed to get this behind us,” said Sen. John Thune (R-S.D.), chairman of the Senate Republican Conference. “We’ve got a lot of work to do.”

Paul Kane and David Nakamura contributed to this report.

Correction: An earlier version of this article misspelled the name of Sen. Jeanne Shaheen.