U.S. shutdown seen dragging on as debt ceiling fight nears

* Fears grow shutdown will last until mid-October

* Budget row gets closer to merging with debt limit date

* Republican-led House prepares more mini funding bills

* Treasury warns of potential "catastrophic" downturn

By Mark Felsenthal and Richard Cowan

Oct 3 (Reuters) - The shutdown of the U.S. government appeared likely to drag on for another week and possibly longer as lawmakers consumed day three of the shutdown with a stalling game and there was no end in sight until the next crisis hits Washington around Oct. 17.

Bowing to the reality that the impasse requires him to remain in Washington, President Barack Obama canceled plans to attend summits in Indonesia and Brunei next week. Earlier this week, he canceled visits to Malaysia and the Philippines because of the shutdown.

Oct. 17 is the date Congress must raise the nation's borrowing authority or risk default, and members of Congress now expect it to be the flashpoint for a larger clash over the U.S. budget as well as President Barack Obama's healthcare law.

The situation gives "every appearance of getting dangerously close to the conversation on the debt ceiling," said Nancy Pelosi, the Democratic minority leader of the House of Representatives.

In fact, she said, "We're in the conversation on the debt ceiling."

At the same time, hopes that the debt ceiling fight could be resolved without a catastrophe were raised by reports in The New York Times and Washington Post that House Speaker John Boehner told other lawmakers he would work to avoid default, even if it meant relying on the votes of Democrats, as he did in August 2011.

A spokesman for Boehner would neither confirm nor deny the reports, restating previous public statements by the speaker that "the United States will not default on its debt."

Senator Charles Schumer, the second-ranking Senate Democrat, reacting to the reports, said, "This could be the beginnings of a significant breakthrough."

The New York senator added, "Even coming close to the edge of default is very dangerous," as he urged quick passage of legislation to raise the $16.7 trillion cap on borrowing.

There was little action along with the talk on Thursday. The Republican-controlled House continued what has become a long process of voting to fund publicly popular federal agencies - like the Veterans Administration, the National Park Service and the National Institutes of Health - that are now partially closed.

Republicans know that neither the Democratic-controlled Senate nor Obama will go along with such an approach, but it allows them to accuse Democrats of working against the interests of veterans, national parks and cancer patients.