A pair of immigrant teenagers confronted Speaker John Boehner (R-Ohio) at a Capitol Hill diner on Wednesday morning, telling him their parents were in danger of deportation because of the House’s inaction on immigration reform.

Boehner was eating breakfast at Pete’s Diner — his regular morning pit stop — when Carmen Lima, 13, and Jennifer Martinez, 16, approached him with a video camera in tow.

After Lima shared her story and asked the Speaker to commit to immigration reform, Boehner told her, “I’m trying to find a way to get this thing done. It’s, as you know, not easy. It’s not going to be an easy path forward, but I’ve made it clear since the day after the election that it’s time to get this done.”

The video of the two-minute conversation was circulated by the Fair Immigration Reform Movement, which is lobbying Congress to pass legislation that includes a path to citizenship for 11 million illegal immigrants.

The House has yet to vote on any immigration reform measures, four months after the Senate passed a comprehensive bill on a bipartisan vote.

Boehner made no specific commitments to the children, and at a press conference hours later, he ruled out passing legislation that could be reconciled with the Senate bill in a conference committee. That was a new marker for the Speaker, and it cuts off what many advocates saw as the only remaining path for the kind of broad immigration overhaul they are seeking.

“We’ve made it clear we’re going to move on a common-sense, step-by-step approach in terms of how we deal with immigration,” Boehner said after a closed-door House Republican conference meeting. “The idea that we’re going to take up a 1,300-page bill that no one had ever read, which is what the Senate did, is not going to happen in the House. And frankly, I’ll make clear we have no intention of ever going to conference on the Senate bill.”

Reform advocates have ramped up pressure on House Republicans, including running television ads in the districts of party leaders and politically vulnerable members. But Boehner’s latest statement is a nod to conservatives who fear that House passage of piecemeal legislation could still lead to a final bill that is similar to the Senate bill, which they consider amnesty.

The House is all but certain not to act in 2013, and the Speaker would not give a timeline for immigration votes.

“Let’s understand something: I want us to deal with this issue,” he said. “But I want to deal with it in a common-sense, step-by-step way.”