Donald Trump made a splashy visit Thursday to the U.S.-Mexico border in a bid to draw attention to illegal immigration. But on the sidelines, he was making news for other reasons -- his threat to mount an independent run for the White House if the Republican Party won't welcome him.

The warning, made in an interview with The Hill, comes as Trump faces some of the toughest criticism yet from fellow Republican candidates. Trump said the Republican National Committee "has not been supportive," and suggested if he does not clinch the nomination and is not "treated" well by Republicans, he'd consider an independent bid.

Asked about the remarks Thursday during his border visit, Trump did not rule out an independent run but said: "I want to run as a Republican. ... I think I'll get the nomination."

Trump's comments immediately raise questions about whether the billionaire businessman and political provocateur -- who is leading several primary polls -- could siphon off votes from a GOP presidential nominee, potentially helping the Democrat. As a self-funded candidate, he would not have to worry about donations drying up if he does poorly in the Republican primaries and caucuses and considers setting out on his own.

Meanwhile, Trump tried to keep the focus Thursday on border security and immigration enforcement. At his border press conference, he said: "I think I'll win the Hispanic vote."

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    The visit was overshadowed not only by his comments to The Hill but by a local Border Patrol union canceling a scheduled meeting shortly before his arrival.

    Hector Garza, president of the National Border Patrol Council Local 2455 chapter, issued a statement Thursday morning saying, "After careful consideration of all the factors involved in this event and communicating with members of the National Border Patrol Council (NBPC) at the National level, it has been decided by Local 2455 to pull out of all events involving Donald Trump."

    He said the border with Mexico is "not secure," and an "honest discussion" is needed with the American people. But he expressed concern that a meeting with Trump would have been portrayed as an endorsement. "As Local 2455, our intentions to meet with Mr. Trump was to provide a 'Boots on the Ground' perspective to not only Mr. Trump, but to the media that would be in attendance at this event," he said. "Just to be clear, an endorsement was never discussed for any presidential candidate. Local 2455 does not endorse candidates for any political office."

    In a written statement, the Trump campaign said the local union was "totally silenced directly from superiors in Washington who do not want people to know how bad it is on the border --- every bit as bad as Mr. Trump has been saying."

    Trump maintained he had been invited by them in the first place.

    The campaign said, "It is unfortunate the local union of Border Patrol Agents received pressure at a national level not to participate and ultimately pulled out of today's event."

    The Trump campaign's original itinerary said he would meet with the Local 2455 Executive Board. He was also meeting with local law enforcement, including federal agents from several agencies.

    The visit comes as Trump both rises in the Republican primary polls and battles criticism from both sides of the aisle for recent comments -- first, for calling some Mexican illegal immigrants "rapists," and then, for questioning Sen. John McCain's "war hero" reputation over the weekend.