* Facing revolt, Senate Republicans delay vote on bill
* Alphabet falls after record EU antitrust fine
* Consumer confidence rises more than expected in June
* Indexes down: Dow 0.15 pct, S&P 0.40 pct, Nasdaq 1.04 pct (Updates to late afternoon)
June 27 (Reuters) - Wall Street dropped on Tuesday as big tech names weighed and losses steepened after a healthcare bill was delayed in the U.S. Senate, raising fresh questions about President Trump's domestic agenda.
Major indexes fell to session lows after U.S. Senate Republican leader Mitch McConnell decided to put off a planned vote on a bill to dismantle the Affordable Care Act until after the Senate's July 4 recess.
The healthcare legislation, which has encountered resistance from several Republicans, is the first plank of Trump's domestic policy agenda, with investors eager for him to move onto his other plans including tax cuts, infrastructure spending and deregulation.
Promises for such domestic polices helped fuel a 13.5 percent rise for the benchmark S&P 500 since Trump's Nov 8 election.
The market likes certainty, and now theres uncertainty," said Peter Costa, president of trading firm Empire Executions in New York. "What is this going to look like when this gets out of the next iteration? That uncertainty I think is just having people pause a little bit."
"I also think that when the market gets to certain levels, any type of uncertainty, especially in anything that has to do with the administration, will have an adverse effect," Costa said.
The Dow Jones Industrial Average fell 33.16 points, or 0.15 percent, to 21,376.39, the S&P 500 lost 9.69 points, or 0.40 percent, to 2,429.38 and the Nasdaq Composite dropped 65.14 points, or 1.04 percent, to 6,182.01.
Big tech names weighed most heavily on the S&P 500. Google parent Alphabet fell 1.8 percent after EU antitrust regulators hit the tech giant with a record $2.7 billion fine.
The tech sector, which has led the market's gains this year, pulled back 1.1 percent.
The healthcare sector weakened after news of the vote delay, and was off 0.5 percent.
Financials were the best performing group, rising 0.9 percent.
Data showed consumer confidence for June rose more than expected, which could bolster the Fed's case for another rate hike this year.
Philadelphia Fed President Patrick Harker said the Fed rightly plans to raise rates once more this year, given recent inflation weakness is likely temporary.
U.S. Federal Reserve Chair Janet Yellen said she does not believe that there will be a run on the banking system at least as long as she lives.
Investors are gearing up for second-quarter corporate earnings season, after a strong first quarter.
"On an earnings basis, the market appears to be fully valued and we need to see fiscal policy, tax and regulatory reform, to drive GDP growth and then stock prices," said Ernie Cecilia, chief investment officer of Bryn Mawr Trust in Bryn Mawr, Pennsylvania.
Declining issues outnumbered advancing ones on the NYSE by a 1.37-to-1 ratio; on Nasdaq, a 1.43-to-1 ratio favored decliners. (Additional reporting by Tanya Agrawal in Bengaluru; Editing by Nick Zieminski)