NEW YORK, Sept 10 (Reuters) - U.S. Treasury yields were

roughly unchanged on Tuesday ahead of a U.S. presidential

candidates' debate and before Wednesday's release of inflation

data, which could fuel speculation on the size of the Federal

Reserve's first interest rate cut.

Republican U.S. presidential candidate Donald Trump and

Democratic Vice President Kamala Harris will meet in their first

and perhaps only debate later on Tuesday, in a clash that could

prove pivotal in their battle for the White House.

The debate will likely refocus the bond market on the

election and the policy implications of the candidates, BMO

Capital Markets Rates Strategists Ian Lyngen and Vail Hartman

said in a note, adding this could lead to higher yields.

"The presumption of upward pressure on yields is a function

of the fact that in either case (Harris or Trump), the next

President will continue to allow deficit spending that requires

funding in the Treasury market," they wrote.

"Supply isn't the largest influence in the US rates market,

but it's certainly a relevant one as 'the deficit hawk' in

Washington DC has become an endangered species - if not

completely extinct."

Harris' late entry in the presidential race after President

Joe Biden's withdrawal in July tightened the race, prompting a

reversal of bond trades that were put in place on expectations

of a second Trump presidency, which had led to higher U.S.

Treasury yields on expectations of higher inflation and wider

budget deficits under Trump.

However, Wednesday's consumer price data could outweigh any

short-term reaction to the debate, with an acceleration in the

pace of disinflation in the economy potentially strengthening

the case for a 50 basis point cut by the U.S. central bank at

its Sept. 17-18 meeting.

Rates traders on Tuesday were assigning a 73% probability to

a 25 basis point cut, up from 62% a week earlier and from 70% on

Monday, CME Group data showed.

"If inflation comes pretty meager ... that would make the

Fed more open to a 50 basis point cut, but if it comes hotter

than expected, 25 basis points is an easier choice," said Matt

Miskin, co-chief investment strategist at John Hancock

Investment Management.

Benchmark 10-year yields were last at 3.685%,

slightly lower than on Monday. Two-year yields stood

at 3.643%, about two basis points lower.

Later on Tuesday the Treasury will sell $58 billion in

three-year notes. This will be followed by sales of 10-year

notes and 30-year bonds on Wednesday and Thursday, respectively.