Sen. John Cornyn John Cornyn'Top Chef' star Tom Colicchio presses Congress to boost SNAP benefits during pandemic NJ governor designates Juneteenth as state holiday The Hill's Morning Report - Sponsored by National Industries for the Blind - Prudent or 'pathetic'? GOP senators plan to vote on coronavirus relief Thursday MORE (R-Texas) on Tuesday seemed to take a veiled shot at President Trump's call for a "good shutdown" of the government.

"Our voters, the people who elected Republican majorities in both Houses and elected this president, did not vote for us in order to shut down the government. They voted for us to govern, as hard as it is," Cornyn said from the Senate floor.

Cornyn, the No. 2 Senate Republican, didn't specifically address Trump's tweet calling for "a good 'shutdown' in September."

Asked specifically about Trump's comments after his speech, the Texas Republican said there had been pro-shutdown comments "from a number of people, from a number of sources."

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Cornyn added during his speech that a shutdown is "basically an abdication of responsibility, particularly if you're in the majority" as Republicans are in both the House and Senate.

"We were elected to govern. Yes, governing is hard. It's hard by design. ... But that's the way our founding fathers designed our constitutional system," he said.