"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."
And the Texas Republican pushed back on Trump call to change the Senate rules.
"The rules have saved us from a lot of really bad policy, even when we were in the minority," Cornyn said.
Trump suggested the US may "need" a shutdown of the federal government in September unless the Senate abolished the filibuster, a tweet which has followed months of frustration for Trump in the Capitol.
Trump's latest comments on Twitter come as the success of the Republican health care bill hangs in the balance in the House -- with House Republican leaders admitting behind closed doors they do not yet have the votes yet to pass one of Trump's signature priorities.
It also follows after Republican and Democratic negotiators agreed on a spending bill that will avert a shutdown and keep the government open, through September -- but leaves out some of the top priorities for the Trump administration, including paying for a border wall and ending federal funding to Planned Parenthood.
Democrats sharply criticized the President's remarks, including Senate Minority Leader Chuck Schumer, who said he was "deeply disappointed" by Trump's suggestion.
"The President has been complaining about the lack of bipartisanship in Washington," the New York Democrat said in a statement. "Well, this deal is exactly how Washington should work when it is bipartisan: both parties negotiated and came to an agreement on a piece of legislation that we can each support. It is truly a shame that the President is degrading it because he didn't get 100% of what he wanted."
Sen. Brian Schatz tweeted in response to Trump moments after the comments came out, saying, "The President just called for a government shutdown this fall. No President has ever done anything like this."
Sen. Patty Murray, the top Democrat on the Senate health committee, called Trump's comments "dangerous and irresponsible."
"President Trump may not like what he sees in this budget deal, but it's dangerous and irresponsible to respond by calling for a shutdown. Hopefully Republicans in Congress will do for the next budget what they did for this one: ignore President Trump's demands, work with Democrats, and get it done," Murray said in a statement Tuesday.
"Maybe some of the victories we had in this omnibus (spending bill) is maybe getting under the Pesident's skin," said Rep. Joe Crowley, the chairman of the House Democratic Caucus, said Tuesday in response to Trump's tweet.