By Jon Keller

BOSTON (CBS) – As the U.S. House prepares to move the impeachment process forward, the political battle surrounding it is intensifying. And the political spin is coming fast and furiously.

Are the Democrats denying President Trump due process, as he and his allies insist? Are the Democrats insulated from political risk by rising public support for impeachment?

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Those are two current claims that don’t have the facts behind them.

“House Democrats’ inquiry, thus far, has been conducted behind closed doors,” complains Senate Majority Leader Mitch McConnell. “They have denied President Trump basic due process rights and are cutting his counsel out of the process in an unprecedented way.”

It’s been the common theme of the GOP impeachment backlash: that President Trump isn’t getting the legal rights that both Presidents Clinton and Nixon enjoyed when they were impeachment targets.

But that’s not true.

The Constitution leaves it up to the House to decide its process, and right now, it’s conducting the equivalent of a grand jury probe, which excludes the participation of potential defendants.

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Meanwhile, the president is on Twitter, urging his defenders to go after the substance of the impeachment push – that phone call with the Ukrainian president that he calls “totally appropriate.”

But while ardent impeachment backers like presidential candidate Tom Steyer insist rising support for impeachment minimizes any political risk for Democrats, that claim is premature at best.

In a new national poll from Suffolk University and USA Today, crucial independent voters are sending up a warning signal.

Only 22 percent say the House should impeach Mr. Trump. Thirty-four percent say go ahead and investigate but don’t impeach, while 36 percent of independents want Congress to drop the whole thing.

And on the “substance?” Less than a third say that infamous phone call strikes them as an impeachable offense.

The bottom line is that independent voters will almost surely make the difference in next year’s election. They’ve been very disapproving of the president’s act, but they’re also skeptical about the Democrats – that’s why they’re not enrolled in either party.

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Keep an eye on how they’re reacting for a good gauge of the political fallout from impeachment.

Jon Keller