Speaker John A. Boehner (R-Ohio) said Tuesday that the fight Republicans are waging against President Obama in the debate over funding the Department of Homeland Security is not about immigration, but rather executive overreach.

"This is not about, actually, the issue of immigration," said Boehner after a closed-door meeting with rank-and-file Republicans. "What it is: It's about the president acting lawlessly."

The speaker's language illustrated the difficult balancing act Republicans face when it comes to talking about immigration. Some Republicans have blamed the GOP's poor performance among Hispanic voters in recent elections on adopting too conservative a posture on border security and citizenship. As the House prepares to pass a very conservative bill to change immigration policy, Republicans risk further alienating those voters.

Boehner added: "Our goal here is to fund the Department of Homeland Security. Our second goal is to stop the president's executive overreach."

The House plans to pass legislation this week that would fund DHS through September and block spending for Obama's executive actions that halt the deportations of millions of undocumented immigrants and give temporary protection to some people brought into the country as children.

The bill is expected to pass along party lines in the House but is expected to meet resistance from Democrats and moderate Republicans in the Senate.

Democrats blasted Republican plans to proceed with votes on five amendments designed to strip away changes in immigration policy made by the Obama administration to protect “dreamers” – or the offspring of illegal immigrants who came to the United States as young children; and to focus on deporting criminal immigrants.

“I never thought they'd go after everything, every protection that has been issued in the last five years,” Rep. Luis Gutierrez (D-Ill.) said Tuesday morning during a rally on the steps of the U.S. Capitol. The Illinois Democrat is a vocal proponent for immigration reform and is launching a 10-city tour in the coming days to build public awareness about the changes to immigration policy ordered by Obama.

Rep. Bennie Thompson (D-Miss.), ranking Democrat on the House Homeland Security Committee, said that Republicans are doing “just what we thought would happen. Now we're picking on children, now we're picking on individuals who really can't defend themselves.” He faulted Republicans for supporting proposals “clearly designed to placate the extreme right wing of their party.”

Boehner was also asked about the possibility that Mitt Romney will run for president again. He declined to opine on the prospect.

"I'll let him make that decision," Boehner said. "There will be a lot of candidates making announcements in the coming months, I expect. It's a very open process. May the best person win."