President Obama’s decision to nominate federal appeals court Judge Sonia Sotomayor to the Supreme Court may help him delay a thornier challenge: what to do with millions of illegal immigrants living in the United States.

The nomination of the first Hispanic justice drew praise Tuesday from the Latino community at a time when many are growing anxious over inaction on broad legislation that would put illegal immigrants — most from neighboring Mexico — on a path to citizenship. Hispanic lawmakers have been pressing Obama to deliver for a key demographic that helped put him in office, with immigration reform the top priority.

The White House has yet to commit fully to taking up broad immigration policy changes this year, with Obama instead pushing forward in tough fights over healthcare, climate change and closing the military prison at Guantánamo Bay, Cuba. Former President George W. Bush twice failed to enact “comprehensive immigration reform” and Obama has kept a relatively low profile on the topic. While many advocates say the two are not directly related, some admit Obama has bought himself a little time with the nomination.

“The Latino community — and not just Latinos, but anyone who’s had a set of life experiences like Sotomayor — will always remember Barack Obama for this,” said Rep. Xavier Becerra (D-Calif.), vice chairman of the Democratic Caucus and the only Hispanic in House leadership. “This will inspire people who were hungry to see a reform of our broken immigration system to stand behind the president on this issue and behind the decisions he makes.”

Senate Democrats and allied interest groups say they’re committed to legislation by the end of Obama’s first year in office. But the stark realities of the calendar, the harsh politics of the issue and unemployment figures nearing double digits are fully within view. Even some of the movement’s biggest advocates are lowering expectations, saying much depends on Obama’s desire to enact sweeping healthcare changes and the president’s own popularity in the months ahead.

Obama is set to hold a high-profile meeting on immigration with key lawmakers June 8, but the congressional calendar is already bogged down with complicated legislation. Any effort on immigration must overcome the politics that shreds party unity on the issue and the grassroots opposition from talk radio and cable television that helped kill Bush’s attempts.