Surrogates for U.S. President Donald Trump were in damage-control mode on Sunday's morning shows after a week of political traumas for the White House.

The escalating impeachment inquiry, the consequences of the decision to pull U.S. troops out of Syria and outrage over a now-reversed plan to host the next G7 Summit at a struggling Trump golf resort have led even normally silent Republicans to voice concerns.

Mulvaney backtracks 

Acting White House Chief of Staff Mick Mulvaney, who added to Trump's woes with a headline-filled news briefing on Thursday, told Fox News Sunday that there had been no quid pro quo between the president and Ukraine.  

Mulvaney had briefed reporters on Thursday that Trump's decision to withhold 391 million U.S. dollars in aid to Ukraine was linked in part to his desire for an investigation by Kiev into a debunked theory that a Democratic National Committee computer server was held in Ukraine.

When told by a reporter that what he had just described was a quid pro quo, Mulvaney responded: "We do that all the time with foreign policy."

The remark left the president's Republican allies frustrated. However, Mulvaney later retracted the comment and on Sunday insisted: "I never said there was a quid pro quo because there isn't."

Mulvaney, who Democrats may yet call before Congress, also said he "absolutely, positively" had not offered to resign. "I'm very happy working there," he said. "Did I have the perfect press conference? No."

Secretary of State Mike Pompeo supported Mulvaney in an interview with ABC's This Week, saying he had not seen evidence of a connection between withholding Ukraine aid and Kiev pursuing an investigation into the DNC server or Trump's political rival Joe Biden.

Pompeo and Graham back Trump

Pompeo also defended the decision to withdraw U.S. troops from northern Syria, a move that opened the door to a Turkish offensive in the region and led to bipartisan accusations the U.S. had betrayed the Kurds and undermined American credibility. 

Mitch McConnell, Senate majority leader, criticized the decision last week, describing it as a "grave strategic mistake" in a Washington Post column. 

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However, Republicans moved to support Trump on Sunday. Senator Lindsay Graham, initially a vocal critic of the president's decision on Syria, told Fox News that he now believed "historic solutions" were possible.

"I am increasingly optimistic that we can have some historic solutions in Syria that have eluded us for years if we play our cards right," he said.

Trump in 'hospitality business'

Mulvaney told reporters on Thursday that the G7 Summit in 2020 would be held at Trump's golf resort in Doral, Florida, sparking outrage from Republicans and Democrats alike.

Critics accused Trump of using his position to enrich himself and his business. The Doral resort is unusual in that it is wholly owned by the Trump organization, which the Washington Post reported took out a 125-million-U.S.-dollar loan to buy and renovate the complex. It has suffered a 69-percent drop in operating income since 2015.

Late on Saturday night, Trump tweeted that the summit would be held elsewhere, blaming "media & Democrat crazed and irrational hostility" for the reversal.

Mulvaney said on Sunday that the president was "honestly surprised at the level of pushback," adding that the president "still considers himself to be in the hospitality business."

Republicans speak out

The chief concern for Trump as the impeachment inquiry progresses is the attitude of fellow Republicans – if he can keep senators on side, he has a safety net against conviction.

There have been few cracks in the Republican 'red wall' in the Senate, but on Sunday Mitt Romney, the Utah Senator and former presidential candidate, told Axios on HBO that it was "shocking" and a "mistake" that Trump publicly asked other countries to investigate Joe and Hunter Biden.

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Graham, a loyal ally on most issues, indicated he could consider impeachment if more evidence emerged in an interview with Axios.

"If you could show me that, you know, Trump actually was engaging in a quid pro quo, outside the phone call, that would be very disturbing," he said.

(With input from Reuters)