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Ex Rubio aide: Trump’s ‘Dumpster fire’ may burn Republicans

It's time for Republican candidates to run their own campaigns — irrespective of Donald Trump, said the former campaign manager of Marco Rubio's unsuccessful 2016 presidential bid.

Terry Sullivan told CNBC's "Squawk on the Street" on Tuesday the race for the White House is no longer about defending or being distracted by Trump — especially now that the candidate has declared himself unshackled:

The Trump "Dumpster fire," as Sullivan described it, came in the form of a tweetstorm Tuesday morning, after House Speaker Paul Ryan said he would no longer defend the Republican candidate in the wake of the lewd "Access Hollywood" tape.

Reacting to the tweets, Sullivan said: "I'm a little shocked that Donald Trump feels like he's somehow been restrained or disciplined until now."

Republicans running for office should determine their stances on Trump on a case-by-case basis, Sullivan advised, and stressed the party's ultimate goal should be to keep control of the Senate and not lose too many seats in the GOP-led House of Representatives.

"I don't know that Trump has anything to lose at this point," said Sullivan, a founding partner of the public relations firm Firehouse Strategies. "But there are a lot of good Republicans out there that do ... not just in Senate and congressional races, but all the way down the ballot."

For the Democrats, strategist Al Motter told "Squawk on the Street" in the same interview the focus for Hillary Clinton needs to remain on campaigning.

"The time is not for gloating. The time is to double down on our ground game and try to increase the margin of victory in November," said Motter, a top bundler for Clinton's National Finance Committee.

Both Clinton and Trump on Tuesday will be campaigning in the swing state of Florida, the home state of Sen. Rubio.