House Republican leadership’s outreach to the Hispanic community ran smack into a tea party wall on Wednesday.

Outside the Capitol, a tea-party-fueled rally on immigration put the spotlight on the dilemma facing Speaker John A. Boehner. The Ohio Republican met with the Congressional Hispanic Caucus on Wednesday and hopes to cure his party’s huge demographic challenge with Hispanics by passing an immigration overhaul this year. But the tea party energy on display outside the Capitol, which catapulted him into power in 2010, has turned on the speaker.

The contrast was on full display at an ill-timed news conference held by GOP Conference Chairwoman Cathy McMorris Rodgers of Washington outside the Capitol in the House Triangle, competing with the larger, daylong anti-immigration-bill news conference and rally on the East Front.

McMorris Rodgers had gathered faith-based leaders of the Latino community on Capitol Hill to, she said, talk about “our shared goals for America” with a half-dozen of her colleagues as part of a larger outreach effort.

At one point, Rep. Mario Diaz-Balart, R-Fla., addressed Hispanic media outlets in Spanish — only to get heckled.

“If they all learned English …” someone shouted from the sidelines, then trailed off, as a woman arrived wielding a sign that read, “Do not reward criminals, no amnesty for illegal aliens!!!”

The speakers sought to brush it off.

“I want to make a call for unity,” said Becky Keenan, a pastor with the Gulf Meadows Church of Houston, Texas, “a call for a tone that is civil, where we can discuss issues, see where we can compromise.”

Across the East Front lawn, a woman was shouting wildly into a much louder microphone, almost drowning out Keenan. Protesters wore T-shirts emblazoned with American flags and tea party slogans, and they waved homemade signs that read, “John Boehner: no amnesty, get a backbone,” “Boehner: go home,” “exporting illegals = importing jobs for Americans, stop socialism,” and “if we lose rule of law we become Mexico.”

Earlier, a mention of Boehner’s name brought a chorus of boos.

The rally against the Senate’s immigration bill and any House bill that would provide a pathway to citizenship before securing the border — organized by Republican Rep. Steve King of Iowa — rallied the base of tea party Republicans and libertarians already in town for a protest on the West Front against the IRS.

The two gatherings featured an overlap of speakers in terms of members of Congress, political activists and public figures such as radio hosts Glenn Beck and Laura Ingraham.

King – along with Republican Reps. Louie Gohmert of Texas, Michele Bachmann of Minnesota, Rob Bishop of Utah and Jack Kingston of Georgia, among others, took to the microphones to denounce anything smacking of “amnesty.”

Gohmert said Wednesday morning that some Republicans, such as those in leadership, are “pandering” to Latinos.

“Maybe we won’t get the Latino vote initially,” he said in an interview with a Latino news outlet, “but once they examine who really cares … which party … wants you to learn English and be the president of the company and [not] relegated to digging a ditch the rest of your life … that’s us.”

At the immigration rally, participants cheered on a reporter who identified himself as affiliated with the conservative outlet Breitbart News, but they booed and heckled a CNN Radio scribe who queried Heritage Foundation fellow Robert Rector about the Congressional Budget Office’s findings that the Senate’s immigration bill would yield big deficit reductions.

Rector blasted the CBO as “the wizard in ‘The Wizard of Oz’” for an incomplete, bells-and-whistles analysis, as members of the crowd called for the legislative branch agency to be abolished. Meanwhile, a group of young women stood in front of the Capitol dressed in the iconic ruby slippers and gingham dresses of Dorothy Gale, the famed protagonist of “The Wizard of Oz.”

Their presence was entirely coincidental: They said they worked at a “Wizard of Oz” museum in Liberal, Kan., and were on a trip to meet their representatives in Congress, for which they had raised money themselves.

Many members, meanwhile, defended themselves against charges that Republicans lack compassion.

“I believe in the dignity of every human person,” King told CQ Roll Call. “That is not just a judgment call, it is in the core of my being. And I believe in the rule of law.”

Meanwhile, after meeting with Boehner, Rep. Luis V. Gutierrez, D-Ill., a leading advocate of an immigration overhaul, talked hopefully.

“I think today we made strong headway,” he said. “I can tell you that I left that meeting with the understanding that there needs to be a majority of Republicans and a majority of Democrats … to come together so the House of Representatives can work its will.”

At McMorris Rodgers’ news conference, however, it was difficult to imagine how the GOP will manage to avoid splintering over the issue. As her group wrapped up and dispersed, Keenan turned and faced a man who shouted, “Oh, I lack compassion, right? You shit on the Constitution all day long!”

“I think a lot of what they are saying is fear-based, really,” Keenan reflected to a reporter, “and there’s a lot of misinformation and ignorance and I understand that that fuels some of these opinions.”

“This image of the Latino coming in and taking away just is just inaccurate. It’s a bit unfair, too, really. … We’re not asking for a free ride. We want border security.”