Story highlights Donald Trump tweeted earlier on Tuesday that a shutdown might help the US in the fall

Members of Congress from both sides of the aisle made an issue of the President's remarks

(CNN) Sen. Orrin Hatch criticized President Donald Trump Tuesday over his call to end the filibuster, saying the US "would have gone straight to socialism" without the Senate rule.

"He apparently hasn't served in a legislative body because had we not had the filibuster rule this country would have been gone a long time ago -- would have gone straight to socialism," the Utah Republican told CNN Tuesday.

Hatch also cautioned Trump against being lulled into thinking the politics of a shutdown would be good for him and other Republicans.

"I think that may be wishful thinking on his part because shutting down the government is not going to work. Republicans always get blamed even though the Democrats are big part of the shutdown and that just doesn't work," Hatch said.

Senate Majority Whip John Cornyn pushes back on Trump's call for a shutdown: "There have been comments from a number of people from a number of sources of shutdown being a good tactic. I just don't agree."

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