This doesn't quite refer to congress as a whole, however it is an example of the opposition undermining a standing president so it may still be what you're looking for. During the Vietnam war the U.S. actually came very close to a settlement with the South and North Vietnamese governments by 1968. It had been difficult to get the peace talks to begin working effectively, particularly due to the obstinance of the South Vietnamese dictatorship under Thieu. However as 1968 wore on and the U.S. Election came closer, it seemed that the democrats would be well on their way to securing an honourable exit to Vietnam and their candidate Humphrey would win the election. Nixon the republican candidate had set himself up as the man with a 'secret plan' to end the war, he had no such plan, but the democrats diplomatic success was a threat to his campaign. He therefore contacted Thieu secretly and offered him a better deal and $250,000 up front if he held out for a republican victory and accused standing president LBJ of lying about the success of the peace talks. Thieu took the deal, Nixon won the election and the Vietnam war ground on for another 6 years. This is now fairly common knowledge and should be in any modern overview of the war, however I know that Kevin Ruane discusses it in 'The Vietnam Wars' and 'War and Revolution in Vietnam'. I'm sure others here can talk about this in more detail and with greater clarity, as there are lots of folks interested in the Vietnam war, but it seemed like a good parallel to your example.
Perhaps not precisely like this, but congress has certainly exerted its power before. A couple examples come to mind, but the Senate Rejection of the Treaty of Versailles is among the times Congress has gone the farthest in foreign policy.
In January 1918 Wilson put forward his 14 points, setting out his views on what the post-war peace should look like. He made this speech without any prior consultation with the british or french governments, and their reaction was a bit incredulous. Clemenceau famously said "But the good lord only had 10!"
However, what happened was kind of interesting. Wilson's 14 points speech was widely distributed, essentially as a piece of propaganda, telling the Central powers that there could be a just settlement to the war, and the treaty would not be unfair. However, when the Germans agreed to an armistice roughly 10 months later, referencing the 14 points, the French and British were caught aback a bit, and were more or less forced to at least consider them a starting point, because the 14 points had been the only public pronouncements of any kind of post-war policy. Even though Wilson personally participated in the negotiation of the Treaty of Versailles, he was ill for some of the negotiations, and the French and British were able to advance many key demands that involved weakening Germany and other concessions. However, the treaty still contained a core of what Wilson had proposed, with the league of nations at its center.
As a backdrop to this in US domestic politics, Republicans took control of the US senate after the election of 1918, and Henry Cabot Lodge was the US Senate Majority Leader, and the leader of the Foreign Relations Committee.
Lodge and Wilson had a poor relationship. Lodge had approached Wilson after the Armistice but prior to the Paris Peace Conference and asked that Republican Senators be included in the US delegation to the peace conference. Wilson refused, appointing all his own people for the delegation. Later, towards the end of the conference, Wilson released the negotiated treaty to the public without consulting with or providing advance notice to the senators who would approve the treaty.
Lodge's response was a public speech on the floor of the senate opposing the treaty. He articulated a view of the United States markedly different from Wilson's internationalist view, one which had much more room for muscular foreign policy.
The United States is the world's best hope, but if you fetter her in the interests and quarrels of other nations, if you tangle her in the intrigues of Europe, you will destroy her powerful good, and endanger her very existence. Leave her to march freely through the centuries to come, as in the years that have gone. Strong, generous, and confident, she has nobly served mankind. Beware how you trifle with your marvelous inheritance; this great land of ordered liberty. For if we stumble and fall, freedom and civilization everywhere will go down in ruin.
This particular act, the public pronouncement of a sitting senate majority leader that he had serious issues with a treaty the president had negotiated, and a pronouncement that, essentially, he would not approve it, is about as close to the present scenario as I can think of.
The Senate ultimately was never able to obtain a 2/3rds majority vote necessary to approve the treaty of Versailles. (Although it was not so simple as Lodge saying "no," because there were multiple attmpts at votes, cloture votes, and other procedural issues). But the senate rejection of the Treaty of Versailles was a pretty stunning rejection of Wilson's foreign policy, and one at that time, that was fairly unprecedented.
The closest thing to undercutting in foreign affairs I can recall is Congressional abstinence to Roosevelt's efforts in the preamble to WWII.
After WWI the United States government and populace was mostly isolationist and war weary, as the Axis powers grew more aggressive President Roosevelt began to gear the country up for war knowing full well that Hitler wouldn't stop at a few territories.
Congress decided to handicap his efforts to remain in line with American ideals as best they could by upholding the Neutrality Acts passed in the 1930's post WWI. Eventually after enough submarine attacks from Nazi's and the attack on Pearl Harbor they changed their minds.
Neutrality act that was a direct response to Roosevelt's attempt to help Britain