In late morning European deals, the euro jumped to $1.1560 -- the highest level since May 2016.
The pound retreated on official data showing annual British inflation unexpectedly slowed to 2.6 percent in June, dimming the prospect of a Bank of England interest rate hike any time soon.
Since Trump's election victory in November, the dollar has soared along with global markets on hopes his big-spending, tax-cutting policies would fire up the world's top economy and fan inflation.
But seemingly never-ending crises have hobbled his presidency from the start, with opposition to Trump's controversial health care reforms -- crucial to freeing up cash -- raising questions about his ability to push through other big-ticket measures.
"The US dollar dived overnight as Donald Trump could not get enough votes from his own party in order to bring in the healthcare reforms he wanted," said CMC Markets analyst David Madden.
While Republicans have 52 of the Senate's 100 seats, the opposition to the bill from two members last week was followed Monday by two more. Their decision means the bill has no chance of even getting a vote unless Senate Majority Leader Mitch McConnell makes significant changes to woo sceptics.
"The US dollar sell-off has intensified further overnight following the announcement from Senate majority leader Mitch McConnell that efforts to repeal and immediately replace Obamacare will not be successful," said currency analyst Lee Hardman at The Bank of Tokyo-Mitsubishi UFJ in London.
"The Republicans have fallen short of the votes required to pass the legislation in the Senate. It is a significant blow to the Trump administration and will further dampen expectations over their ability to pass current plans for comprehensive tax reform in a timely manner."
The dollar came under pressure as traders eye the Federal Reserve's timetable for raising interest rates, while Trump struggles and inflation remains subdued.
Recent remarks from Fed boss Janet Yellen indicating the bank will concentrate on prices have tempered rate expectations in recent weeks.
The euro has broken above the $1.15 mark for the first time since last June, with eyes on the European Central Bank's policy meeting this Thursday.
While ECB chief Mario Draghi is not yet expected to announce any tightening measures, there is speculation the central bank will begin winding down its stimulus programme as the eurozone economy improves.
Euro/dollar: UP at $1.1556 from $1.1479 at 2100 GMT Monday
Pound/dollar: DOWN at $1.3032 from $1.3057
Dollar/yen: DOWN at 112.30 yen from 112.61
London - FTSE 100: UP 0.4 percent at 7,404.10 points
Frankfurt - DAX 30: DOWN 0.6 percent at 12,515
Paris - CAC 40: DOWN 0.2 percent at 5,218.40
EURO STOXX 50: DOWN 0.3 percent at 3,156.50
Tokyo - Nikkei 225: DOWN 0.6 percent at 19,999.91 (close)
Hong Kong - Hang Seng: UP 0.2 percent at 26,524.94 (close)
Shanghai - Composite: UP 0.4 percent at 3,187.57 (close)
New York - DOW: FLAT at 21,629.72 (close)
Oil - Brent North Sea: DOWN 20 cents at $48.71 per barrel
Oil - West Texas Intermediate: DOWN 29 cents at $46.25