Mr Trump's 2018 budget blueprint reportedly includes a 37% spending cut for the State Department and US Agency for International Development (USAID).
He will set out to convince Congress of his proposal in his first address to a joint session on Tuesday night.
But Republican Senator Lindsey Graham said his plan is "dead on arrival".
"It's not going to happen. It would be a disaster. If you take soft power off the table then you're never going to win the war," Senator Graham said.
Soft power is an American term that refers to diplomatic tools such as foreign aid and humanitarian relief.
"What's most disturbing about the cut to the State Department's budget is it shows a lack of understanding of what it takes to win the war," Senator Graham continued.
Senate Majority Leader Mitch McConnell also said Mr Trump's reported deep cuts to the State Department would "probably not" pass Congress.
The Republican-controlled Congress must approve any federal spending.
To the White House, foreign aid might seem like an easy target for cuts, but those who protect the country think otherwise.
In their letter to lawmakers more than 120 former military officers quoted the Defence Secretary James Mattis from his days as a field commander: "If you don't fully fund the State Department then I need to buy more ammunition."
They argued that strengthening diplomacy and development were critical to preventing conflict. International assistance in the State Department budget does more than respond to humanitarian needs, it also supports policy goals.
For example, it supplements the military fight against the so-called Islamic State through programmes to disrupt the group's financing and recruitment, and to stabilise communities where IS has been driven out.
There's money to address the underlying causes of migration from Central America, and to strengthen allies such as Afghanistan and Ukraine.
The former Secretary of State John Kerry was known to make a strong case for increasing the department's financing, (which at $50bn makes up just 1% of the entire budget).
The new Secretary Rex Tillerson will have to fight simply to keep what he has, or the State Department will be marginalised in an administration focused on the military.
The president released a budget proposal on Monday calling for a $54bn (Â£43bn) boost to military spending.
This would be paid for, according to the plan, by gutting other programmes including foreign aid and the environmental agency.
The White House also plans to reduce spending for the State Department and USAID,  say US media reports, which together received an estimated $50.1bn during the current fiscal year, or a little more than 1% of the total federal budget.
More than 120 retired generals have signed a letter urging Congress not to cut funding for diplomacy and foreign aid.
The letter said: "As you and your colleagues address the federal budget for Fiscal Year 2018, we write as retired three and four star flag and general officers from all branches of the armed services to share our strong conviction that elevating and strengthening diplomacy and development alongside defense are critical to keeping America safe."
Development assistance would probably be hardest hit while staff reductions would see fewer security contractors at diplomatic missions abroad, the AP reported, citing officials familiar with the proposal.
The Office of Management and Budget has not yet said where overall reductions would occur.
The Republican pushback over Mr Trump's reported plan comes as the president is set to deliver his first major speech to Congress since taking office.
An address to Congress is a different kind of presidential speech. Will the American public see a different Donald Trump?
If history is any guide, that seems unlikely. Every time there has been talk of a pivot or shift of focus for candidate Trump, or president-elect Trump, or President Trump, the end result has been the same Donald Trump as always - blustering and belligerent, unvarnished and unapologetic.
Mr Trump would be well-served to take a different tack tonight, however. While he's spent his first month in office in a blizzard of activity, issuing executive orders and squelching controversies, there's been little progress with his agenda in Congress.
Top-line items like tax cuts and healthcare reform will be heavy legislative lifts with a baulky conservative caucus in the House and a narrow Republican majority in the Senate, requiring presidential leadership of a kind not yet demonstrated by Mr Trump.
Recent opinion polls have shown the president's standing with the public improving after a dismal first few weeks, but any progress can quickly evaporate if his "man of action" bravado runs headfirst into congressional obstinance.
Tuesday night's speech is the president's first major opportunity to avoid that outcome.
He is expected to set out in greater detail his plans to cut spending and boost the economy as well as offer an "optimistic vision" about the "renewal of the American spirit", a senior White House official told the BBC.
At least one Democrat has said he would refuse to shake Mr Trump's hand before the speech, bucking a longstanding bipartisan tradition in presidential first addresses to Congress.
Representative Eliot Engel, a top New York Democrat on the House Foreign Affairs Committee, said he would not shake Mr Trump's hand as he enters the chamber, citing the president's attacks on media and refusal to work with Congress.
It will be the first time Mr Engel has not sought a centre aisle seat to shake the president's hand in his 29 years serving in the House.
Republicans are lining up against President Donald Trump's proposed budget cuts to the State Department, hours before his address to Congress.