(Reuters) - One Republican lawmaker said on Tuesday America should “whack” its Latin American neighbors by cutting aid in response to a flood of undocumented minors entering the United States, while another asked where the children should be "dropped off when the buses bring them back."

As Homeland Security Secretary Jeh Johnson assured U.S. lawmakers the Obama administration is doing everything it can, including dispatching more agents to the Mexican border, the crisis was deepening the stark battle lines between Republicans and Democrats in Washington. The debate adds another hurdle to efforts to pass legislation on immigration reform.

A sweeping immigration overhaul bill passed the Democratic-led Senate last year. But it has stalled in the Republican-led House of Representatives, whose leaders insist President Barack Obama's administration should secure the border before easing immigration restrictions.

They blame the flood of children on Obama's giving temporary relief from deportation to some young people brought illegally to the United States by their parents.

Several Republicans at a House Homeland Security committee hearing sharply questioned Johnson about the crisis, accusing the administration of doing too little to prevent the thousands of illegal arrivals.

Up to 350 children are picked up along the U.S.-Mexico border every day, three-quarters of them from El Salvador, Guatemala and Honduras, Johnson said. Republicans suggested sending in the National Guard and pressing Mexico to beef up its own border security. Separately, House Speaker John Boehner announced a working group of seven Republicans to address the crisis on Tuesday.

Michigan Republican Representative Candice Miller suggested cutting off aid and repealing free trade agreements with Mexico and the Central American countries involved.

"We need to whack them, our neighbors, to understand that they are just not going to keep taking our money and we are just going to be sitting here like this - we're not the ATM machine," she said.

Alabama Republican Mike Rogers scoffed after Johnson said he had discussed the issue with Guatemalan authorities. "I think what you need to do is ask the Guatemalan government where they want these kids dropped off when the buses bring them back down there," Rogers said.

Democrats described the influx as a humanitarian crisis prompted by poverty and gang and drug violence.

Johnson said 115 agents have been transferred to the Rio Grande Valley, and a further 150 may join them.

In the fiscal year ended in September 2013, agents picked up more than 24,000 unaccompanied children at the southern border. That number has already passed 52,000 so far this fiscal year.

"We are talking about large numbers of children, without their parents, who have arrived at our border - hungry, thirsty, exhausted, scared and vulnerable. How we treat the children, in particular, is a reflection of our laws and our values," Johnson said.

He said smugglers, seeking clients, are putting out false information that minors who reach the United States will be allowed to remain. But he said he could not explain the recent surge in arrivals.

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