WASHINGTON — Just hours after the White House released a summary of President Donald Trump's call with the president of Ukraine — in which Trump urged the Ukrainian leader to do him a "favor" — Texas Sen. John Cornyn stood on the floor of the Senate and tore into House Democrats for moving forward with an impeachment inquiry based in part on that call.

"They should be embarrassed by what they have done," said Cornyn, one of the top Republicans in the Senate." Cooler heads will prevail here in the United States Senate."

So far the Senate majority has stood by the president, as Cornyn — along with many of his GOP colleagues — lambasted House Democrats’ move toward impeachment. Cornyn dismissed it as simply “about re-litigating the 2016 election,” while fellow Texas Sen. Ted Cruz called it a "lynch mob."

Both Texas senators were unmoved by a rough transcript of the 30-minute call the White House released Wednesday in which Trump told Ukrainian President Volodymyr Zelensky to work with the U.S. Attorney General to investigate Democratic presidential contender Joe Biden.

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It was one of two critical moments on Wednesday when the Texas senators again sided with Trump — the latest tests of loyalty to a president with whom they have stood by staunchly since he took office. Cornyn and Cruz also again defended Trump’s raiding of military funding to build the border wall, voting against a Senate resolution to end the president’s emergency declaration, which allows his administration to divert the money without congressional approval.

The stakes are highest for Cornyn as he heads into what will likely be the toughest re-election battle of his career in 2020. Democratic challengers are painting the senator as Trump’s crony, pointing to a recent fundraising pitch in which Donald Trump, Jr. called Cornyn his father’s “biggest ally.” That’s a descriptor Cornyn himself didn’t exactly shy away from, telling reporters last week that he would leave it to the Trumps to characterize their relationship, but adding “we do work closely together.”

Several of Cornyn’s would-be opponents went on the attack Wednesday.

“Trump isn’t even attempting to hide his corruption — because he knows he can get away with it,” tweeted Sen. Royce West, one of nearly a dozen Democrats running to challenge Cornyn. “It’s time to impeach. And it’s time to elect a Senator who will stand up to Trump and his enablers.”

“That @JohnCornyn will not recognize that using the Presidency to blackmail others into investigating one’s political rivals is the hall-mark of a bought and paid for politician,” tweeted Houston Democrat Chris Bell, a former congressman.

Poll: 57 percent of voters against impeachment

Cornyn said he wants Congress to continue its “bipartisan” investigations of the call and the whistleblower complaint about it. A Senate Intelligence Committee member, he voted for a resolution that passed unanimously in the Senate on Tuesday calling on the Trump administration to turn over the complaint, which was made available to congressional intelligence committees on Wednesday.

The intelligence committee is set to hear testimony on the issue from the acting director of national intelligence on Thursday.

“That’s exactly how this matter should be handled,” Cornyn said. “By the book, and to make sure that everybody’s rights are protected before people begin to cast unjustified and slanderous allegations.”

For subscribers: Texas Democrats join cascade of impeachment calls

Cornyn told reporters that it's "possible to find some of the conversation troubling without finding it a basis for impeachment." He said Trump was simply asking Zelensky to probe corruption in Ukraine and the idea that Trump was asking him to target Biden specifically is “a too-narrow construction of what’s going on here.”

"I don’t think asking another country to do an investigation into corruption concerns is objectionable," he said.

Cornyn also is convinced voters do not support impeachment — and it appears he’s right, at least for now. According to a Quinnipiac University poll released Wednesday morning, just 37 percent of voters say that Trump should be impeached and removed from office, while 57 percent say he should not be impeached. The poll was conducted from Thursday through Monday, as details were emerging about Trump’s call with Zelensky.

But Trump’s polling in Texas hasn’t been stellar of late, and standing by him could hurt Cornyn in 2020. It’s a political decision Cruz faced last year, when he fully embraced his one-time bitter political rival — a decision that worked out for Cruz in the end.

In the border emergency vote, both Cornyn and Cruz were on the losing side as the Senate voted 54-41 on a resolution to end the emergency declaration, with several Republicans joining the Democrats. The measure will almost certainly be vetoed by Trump.

“How would I square voting differently?” Cornyn said. Cornyn dismissed concerns about his state losing some $38.5 million in funds for projects in El Paso and San Antonio as “way too parochial” and expressed confidence that the money for the Texas projects would ultimately be restored, even though Democrats have insisted they will not go along with that plan.

“There won’t be any net loss, in my opinion,” Cornyn said.

The Democratic Senatorial Campaign Committee on Wednesday released new digital ads targeting Cornyn and several other Senate Republicans, accusing them of “raiding” millions from “military communities.”

“Even as the White House threatens to claw away even more money from their states, these Senators are so craven that they voted to double down on enabling this reckless cash grab,” DSCC spokesman Stewart Boss said in a statement.

This report contains material from the Washington Post and the Associated Press.

ben.wermund@chron.com