As the fiscal crisis subsided and the government went back to work this week, President Obama and other leading Democrats were quick to say that an immigration overhaul should be back on the agenda in Congress.

Mr. Obama raised the issue in his first comments after lawmakers reached a deal to reopen the government, and on the night the shutdown ended the three top Senate Democrats said they hoped to extend the bipartisan moment that produced the compromise by taking up immigration.

“Let’s move on,” said the Senate majority leader, Harry Reid of Nevada. He added that he hoped “the next venture is making sure we do immigration reform.”

But the possibilities for progress on the issue will be determined in the House of Representatives, where many conservative Republicans are fuming with frustration over their meager gains from the two-week shutdown and turning their ire against Mr. Obama, saying he failed to negotiate with them. It will be up to Speaker John A. Boehner of Ohio to discern whether relations with the White House are simply too raw for House Republicans to consider legislation on an issue the president has made a priority.