* Republican push to overhaul or repeal healthcare law hits snag
* U.S. import prices decline for 2nd month
* U.s. 10-year note yield falls to 3-week low (Updates prices, adds comment)
NEW YORK, July 18 (Reuters) - U.S. Treasury yields fell on Tuesday, as investors grew cautious about the latest political drama in Washington around healthcare legislation, with weak economic data adding to the uncertainty about the pace of future interest rate hikes by the Federal Reserve.
Yields on the 5-year, 7-year, and 10-year notes, which move inversely to prices, dropped to three-week lows, while those on the 30-year bond slid to their lowest in two weeks.
Republican efforts to overhaul or repeal Obamacare collapsed in the U.S. Senate on Tuesday, dealing a sharp setback to President Donald Trump and the Republican Party's seven-year quest to kill President Barack Obama's signature healthcare law.
"It does add some uncertainty as to whether the administration and a cooperative Congress is able to push through with priorities that was communicated in the election period," said Bill Northey, chief investment officer at U.S. Bank Private Client Group in Helena, Montana.
Investors fretted about the growing division within Trump's Republican party that has hampered the administration's legislative policy goals.
But Northey said persistently low inflation has been a major driver for the slide in yields the last two weeks.
"Inflation has not materialized in the way that the Fed anticipated and it hasn't manifested in labor costs, commodities, or core inflation," Northey said.
Weak inflation was again evident in Tuesday's economic data, which showed U.S. import prices falling for a second straight month in June as the cost of petroleum products declined further.
In late trading, U.S. 10-year yields fell to 2.266 percent from 2.309 percent late Monday. Yields earlier hit a three-week low of 2.259 percent.
DRW Trading market strategist Lou Brien said the drop below the key 2.30 percent yield on the 10-year was a significant technical indicator that suggested further Treasuries buying. The next key level for 10-year yields would be 2.25 percent, he added.
U.S. 30-year bonds yielded 2.854 percent, from 2.893 percent on Monday. Those yields earlier touched a two-week low of 2.849 percent.
U.S. two-year yields were down at 1.351 percent from Monday's 1.36 percent.
The yield curve continued to flatten on Tuesday, with the spread between five-year and 30-year yields narrowing to 103.50 basis points.
The same was true for the spread between U.S. two-year and 10-year notes, with the gap shrinking to 90.50 basis points , the tightest in two weeks. The spread was last at 91.60 basis points.
In general, a flat yield curve reflects expectations that inflation will decline. (Reporting by Gertrude Chavez-Dreyfuss; Editing by Meredith Mazzilli)