President Obama announced Friday that he has tapped White House aide Katie Beirne Fallon, a veteran Capitol Hill insider, to help steer his legislative strategy on immigration and health care and to advance the administration’s climate policies.

Fallon, a well-regarded policy and political strategist with deep relationships with Democratic lawmakers, will take over as White House director of legislative affairs. She replaces Miguel Rodriguez, a lawyer and former foreign policy aide who was relatively unknown among congressional leaders.

The move comes after a difficult year for Obama’s congressional agenda. In a statement announcing Fallon’s promotion, the president said, “She has the deep expertise and strong relationships required to build on the progress we’ve made this year and advance my top priority: creating jobs and expanding broad-based growth and opportunity for every American.”

Fallon’s promotion will not be the last staff change at the White House. In the past week, Obama has brought on former legislative affairs director Phil Schiliro and Democratic strategist John Podesta for temporary assignments. And the president is searching for a replacement for one of his most trusted aides, White House counsel Kathryn Ruemmler. Ruemmler had planned to return to private practice by the end of the year but has agreed to stay on until spring.

The president is looking for a counsel whom he can rely on for legal advice rather than policy suggestions, according to a senior White House official who asked not to be identified in order to discuss personnel matters. Those qualities are critical, given the ongoing probes championed by House Oversight and Government Reform Committee Chairman Darrell Issa (R-Calif.), the official added, saying Obama wants “someone who can deal with Issa on Oversight.”

The White House also is seeking to fill a few other posts, including the heads of the Office of Cabinet Affairs and the Council on Environmental Quality, in the near future. Podesta, who will help oversee the president’s energy and environmental agenda for one year as senior counselor, will help select the next CEQ chair, the official said.

The move to bolster the legislative affairs shop comes as the White House has brought Schiliro in for a two-to-three-month assignment to oversee the ongoing rollout of the Affordable Care Act and address lawmakers’ concerns about the law.

Fallon was a longtime aide to Sen. Charles E. Schumer (D-N.Y.) and served as staff director for the Senate Democratic Policy and Communications Center, which Schumer and Majority Leader Harry M. Reid (D-Nev.) run, until May 2013, when she joined the White House as deputy communications director.

“There’s nobody — nobody — better suited for this job,” Schumer said in a statement about Fallon. “Katie has the great ability to listen and then bring people together, and will be able to convey the administration’s message in strong but friendly terms to members of both parties.”

Denis McDonough, the White House chief of staff, has been thinking about restructuring the legislative affairs operation to be “more responsive to concerns on the Hill and better calibrated to promote the president’s agenda,” according to a White House official. After consulting with Obama, McDonough proposed moving Fallon into the job. She met with Obama to diagnose the White House’s problems on Capitol Hill, the official said, and Obama asked her to coordinate his climate-change agenda and manage legislative strategy around immigration reform and the health-care law.

Fallon will begin her new assignment in January. An aide said she plans to spend the next few weeks consulting with lawmakers about the 2014 agenda.

“Katie is whip smart, and fully understands the challenges and opportunities members of Congress face every day,” McDonough said in a statement.

Rodriguez, a former Senate aide to Hillary Rodham Clinton who joined the State Department at the start of the Obama administration, is leaving to pursue a job in the private sector.

“Throughout some of this year’s most contentious legislative battles, Miguel worked tirelessly to bridge the partisan divide, forge consensus, and seek out solutions that helped us move forward,” Obama said in his statement. “I’m grateful for his service, and I will miss his advice and counsel.”

Karen Tumulty contributed to this report.