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Democrats blamed Republicans for playing a part in the streams of children coming to the U.S-Mexico border by claiming U.S. border security and immigration are weak.

“Every time that a politician in the United States says that Barack Obama isn’t deporting anybody, every time they say we have open borders,” said Rep. Luis Gutierrez, D-Ill. Thursday, “every time that they say that every child coming here in this humanitarian crisis is going to be able to stay … traffickers say the same thing to their victims and say, “Come. Look. It’s a time.”

The accusations are an attempt to seize and hold the narrative on the children whose arrivals have triggered a government-wide response as immigration opponents have seized the issue to further question President Barack Obama's ability to enforce immigration law.

The tens of thousands of children who have arrived this year have forced officials to look for more room to process and temporarily shelter them and have turned new U.S. attention to its neighboring countries.

Controlling messaging around the children has become key, not only for the two political parties but in an attempt to stem the flow of youths coming from Honduras, Guatemala, Mexico and El Salvador.

For their part, Democrats in a news conference hammered the idea that what the nation is facing is a humanitarian and refugee crisis.

“As chairman of the Foreign Relations Committee, I’m seeing day by day violence in so many countries spreading across the hemisphere, but I never have seen or thought I would see refugees from this hemisphere spilling over our borders,” said Sen. Bob Menendez, Senate Foreign Relations Committee chairman.

Menendez said the stall on immigration reform has played a role. “If they (Republicans) continue to obstruct the Senate bill and do nothing, there will continue to be a reality of trouble on our borders and the refugee problem will only get worse,” he said.

Republicans postponed until next week a hearing originally planned for Thursday on the crisis that labels the children’s arrivals as “administration made.”

Many in the party have blamed the promise of immigration reform, the holds put on deportations of young immigrants by President Barack Obama and policies in place for years in which children are released to families while awaiting deportation processing.

Boys wait in line to make a phone call as they are joined by hundreds of mostly Central American immigrant children that are being processed and held at the U.S. Customs and Border Protection Nogales Placement Center on June 18, 2014, in Nogales, Arizona.Fran / Getty Images

Michigan GOP Rep. Candice Miller has called on Obama to send out the National Guard. She also said in a letter to the president that he has helped feed rumors that children sent to the U.S. will be allowed to stay because he put the deportations of certain young immigrants on hold. The children don’t qualify for either but GOP members say that hasn’t stopped the rumors.

One talk radio host discussing the children played a portion of the old Taco Bell commercial in which a chihuahua is heard saying “You Quiero Taco Bell.”

Meanwhile, Vice President Joe Biden was headed to Guatemala to meet with President Otto Pérez Molina, El Salvador President Salvador Sánchez Céren and a representative of the Honduran government.

U.S. lawmakers also want the Central American countries where the children are from to seize control of the messaging in their countries and do more for the security of their children.

“The governments in Central America have a responsibility to inform the nationals of their country that there is no guaranteed benefit when they come,” Gutierrez said.

Menendez said he is dissatisfied with some of the Central American leaders. “They have to take responsibility as well,” he said. “There are things they have to do in their country to try to create greater citizen security, greater rule of law and greater opporturnity for their citizens.

An official with the El Salvador embassy said the country had researched the attitudes of young people ages 16-24 on making the trek north and found 90 percent wanted to do it.

They devised a pilot campaign focused on three regions of El Salvador warned of the dangers of the journey north. It included a thick comic book, literature, posters and a two-day workshop. The official said there was about a 30 percent drop in interest in migrating to the U.S. after the campaign. The official said the country is looking at extending the campaign.