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WASHINGTON, DC - JULY 09:  U.S. Circuit Judge Brett M. Kavanaugh looks on as U.S. President Donald Trump introduces him as his nominee to the United States Supreme Court during an event in the East Room of the White House July 9, 2018 in Washington, DC. Pending confirmation by the U.S. Senate, Judge Kavanaugh would succeed Associate Justice Anthony Kennedy, 81, who is retiring after 30 years of service on the high court.  (Photo by Chip Somodevilla/Getty Images)
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WASHINGTON, DC - JULY 09: U.S. Circuit Judge Brett M. Kavanaugh looks on as U.S. President Donald Trump introduces him as his nominee to the United States Supreme Court during an event in the East Room of the White House July 9, 2018 in Washington, DC. Pending confirmation by the U.S. Senate, Judge Kavanaugh would succeed Associate Justice Anthony Kennedy, 81, who is retiring after 30 years of service on the high court. (Photo by Chip Somodevilla/Getty Images)
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(CNN) —  

The bruising, partisan battle over the Supreme Court nomination of Brett Kavanaugh has created an “improvement in the political environment” for Republicans running for re-election, the executive director of the largest House GOP super PAC told donors.

Though acknowledging House Republican candidates “still face historic headwinds,” Corry Bliss, the executive director of the Congressional Leadership Fund, the outside group aligned with House Speaker Paul Ryan, credited the posture of President Donald Trump and the White House’s willingness to fight allegations of sexual assault against Kavanaugh with an uptick in GOP numbers.

“The President and the White House have worked aggressively to improve the political environment over the past two weeks, and now CLF must fight district by district to keep the House,” Bliss states in the memo, which was obtained by CNN from a source who received it.

The memo, from the group that has raised $90 million to spend for House Republicans this cycle, addresses one of the key assertions from Republican leaders in the wake of the a fight that turned both deeply partisan and extremely bitter not just in the Senate, but across the country.

While Senate Republican campaigns and GOP advisers have credited the Kavanaugh fight for improving their prospects in several races where Democratic incumbents are seeking to beat back challengers in states won handily in 2016 by Trump, the question of what it would do to House races, where the dynamics are decidedly different, has remained an open one.

“The base is on fire,” Senate Majority Leader Mitch McConnell told reporters shortly after the vote to confirm Kavanaugh. “I was talking to several of my political advisers (Friday) about what we’re seeing out in the red states is a dramatically rising interest.”

For House Republicans especially, any boost in the overall environment would be welcome. But the dynamic in those races, where many of the growing number of at-risk GOP members are facing electorates not dominated by Trump supporters, but instead by suburban enclaves and women voters who have turned sharply against the President.

“You know, they’ve won and perhaps there will some letdown now in enthusiasm,” Sen. Dick Durbin of Illinois, the second ranking Democrat in the Senate, said Tuesday. “I will just tell you, I’m following the House races now in my state and the Democrats are improving throughout this debate and the latest polls show us within striking distance in four different seats.”

Women’s support for Democratic candidates remains extremely strong, according to a CNN poll conducted by SSRS. Sixty-three percent of women say they’ll vote for the Democrat in the midterms and only a third say they’ll vote for the Republican. Men are more closely divided, but tilt in the opposite direction, with half backing the Republican and 45% behind the Democrat.

Democrats remain well ahead of Republicans in a generic ballot matchup, with 54% of likely voters saying they support the Democrat in their district and 41% backing a Republican, according to the poll.

But Ryan, in remarks on Monday, said he too noticed, at least anecdotally, an uptick in Republican base enthusiasm from the Kavanaugh fight.

“I think the Democratic base was already there,” Ryan said at an event at the National Press Club. “This definitely – I could just see it from traveling around the country in the last few days, traveling around Wisconsin – the Republican base is definitely animated after this.”

Bliss, in his memo, said in his group found in uptick in the President’s approval in 20 districts polled during peak of the Kavanaugh fight.

“As the Supreme Court battle unfolded, the enthusiasm gap closed across the country, Republicans improved their standing with independent voters, and President Trump’s job approval rating improved across the board,” Bliss wrote.

But Bliss also acknowledged a series of hurdles, beyond the Democratic voter enthusiasm, House Republicans will have to overcome, from the significant candidate fundraising advantage Democrats have shown in the last quarter to the large number of House Republican retirements that have hamstrung the group’s efforts.