A majority of Americans oppose President Donald Trump's proposed budget increases to the Department of Defense at the cost of other departments, a new poll finds.

A CNN/ORC poll out Wednesday finds 58 percent of respondents oppose the administration's plan to increase military spending by cutting funding for the State Department and other agencies.

The proposal to cut State funding was met with immediate criticism from Republican Sens. Marco Rubio, John McCain and Lindsey Graham.

Graham last week called the pitch "dead on arrival." McCain also criticized the proposed increases in Defense Department spending as not robust enough.

The State Department, in its first briefing since the inauguration, pushed backed Tuesday against assertions that its role was being diminished in the new administration.

Secretary of State Rex Tillerson "is very engaged with the White House, very engaged with the president, speaks to him frequently," acting State spokesman Mark Toner said. "I can assure everyone that the secretary's voice, or the State Department's voice, is heard loud and clear in policy discussions."

Toner explained the thinking internally on the proposed cuts.

"What [Tillerson's] goal, what senior staff's goal here at the State Department is to say, OK where can we possibly move resources to, reevaluate resources, reassess, perhaps make cuts if we feel that's necessary," Toner said.

The president laid out his plan for an expanded Defense budget last week.

"I am sending Congress a budget that rebuilds the military, eliminates the defense sequester -- and calls for one of the largest increases in national defense spending in American history," Trump said in his address to Congress Feb. 28. "The challenges we face as a nation are great, but our people are even greater. And none are greater or braver than those who fight for America in uniform."

But congressional sources told CNN Tuesday that the administration favors a $1.3 billion cut to the Coast Guard to help pay for other Defense expenditures and the construction of an expanded physical barrier on the southern border.

That plan was met with critique by some of Trump's earliest backers, including Rep. Duncan D. Hunter, R-Calif., who represents a military-heavy San Diego-area district.