More Republicans are telling President Donald Trump in ever blunter terms to lay off his escalating criticism of special counsel Robert Mueller and the Russia probe. But party leaders are taking no action to protect Mueller, embracing a familiar strategy with the president — simply waiting out the storm. Trump blistered Mueller and his investigation all weekend on Twitter and started in again Monday, questioning the probe's legitimacy with language no recent president has used for a federal inquiry. 'A total WITCH HUNT with massive conflicts of interest!' Trump tweeted. Mueller is leading a criminal probe into whether Trump's 2016 presidential campaign had ties to Russia and whether there has been obstruction of justice since then. Trump was told to cut it out on Sunday by such notable Republicans as Trey Gowdy, chairman of the House Oversight Committee, and Bob Corker, chairman of the Senate Foreign Relations Committee. Then on Monday he was told that firing Mueller would be 'the stupidest thing the president could do' by Orrin Hatch, chairman of the Senate Finance Committee. But Hatch, on CNN, also said he didn't see any need for legislation to protect Mueller. And that sentiment was widely echoed by GOP leaders. In recent months, bills to protect the special counsel have stalled, and Republican leaders have stuck to muted statements endorsing Mueller or denying he is in trouble. So far, that tactic has worked for them as Trump has lambasted the Russia investigation on Twitter but allowed Mueller to continue his work. Democrats say legislation is needed. 'Immediately,' said Sen. Richard Blumenthal of Connecticut. And Arizona Republican Jeff Flake, a frequent Trump critic, said, 'If you don't pick this fight, then we might as well not be here.' But GOP leaders saw no reason to leap to stop a firing they don't think is in sight. 'I don't think that's going to happen so I just think it's not necessary, and obviously legislation requires a presidential signature,' said Texas Sen. John Cornyn, the No. 2 Republican in the Senate. 'I don't see the necessity of picking that fight right now.' Still, Cornyn said there would be 'a number of unintended consequences' if Mueller were to be removed, and lawmakers had communicated that message to Trump 'informally and formally.' White House lawyer Ty Cobb issued a statement Sunday tamping down the speculation, saying Trump is not 'considering or discussing' Mueller's removal. White House spokesman Hogan Gidley said Trump has 'some well-established frustration' about the probe but insisted there is no internal discussion about removing Mueller. Separately, Trump's legal team has provided documents to Mueller summarizing their views on key matters being investigated, according to a person familiar with the situation. That person insisted on anonymity to discuss the ongoing investigation. The records were given as Trump's lawyers negotiate with Mueller's team about the scope and terms of a possible interview with the president. Also, Trump added a new lawyer. Joseph diGenova, a former U.S. attorney for the District of Columbia, will join his team later this week. DiGenova has been outspoken in his defense of Trump, talking of a 'brazen plot' to exonerate Hillary Clinton in an email investigation and to 'frame' Trump with a 'falsely created crime.' Multiple White House officials said Monday that they believe Trump is now acutely aware of the political — and even legal — consequences of taking action against Mueller. For now, they predicted, Trump will snipe at Mueller from the outside. His sniping is getting more pointed. Trump challenged the probe's existence over the weekend and strongly suggested political bias on the part of Mueller's investigators. The tweets ruffled some GOP lawmakers. South Carolina's Gowdy admonished the president's lawyers, saying that if Trump is innocent, 'act like it.' But House and Senate leaders remained quiet, and decidedly unruffled. 'As the speaker has always said, Mr. Mueller and his team should be able to do their job,' said AshLee Strong, spokeswoman for House Speaker Paul Ryan. A spokesman for Senate Majority Leader Mitch McConnell referred to comments that McConnell made in January saying he wasn't worried that Mueller would be ousted. Two bipartisan Senate bills introduced last summer, when Trump first started criticizing Mueller's probe, would make it harder to fire a special counsel by requiring a judicial review. But Republicans backing the bills have not been able to agree on the details, and Senate Judiciary Chairman Chuck Grassley has shown little interest in moving them. McConnell has said he thinks they are unnecessary. Still, some of the White House officials acknowledged that Trump did once flirt with removing Mueller. That came last summer, when Trump's legal team — then led by New York attorney Marc Kasowitz — was looking into potential conflicts of interest with Mueller and his team and planning to make a case to have him removed, according to people familiar with the strategy. Those people spoke on condition of anonymity to discuss the private conversations. As that strategy was being formulated, Trump directed White House counsel Don McGahn in June to call Deputy Attorney General Rod Rosenstein to raise the perceived conflicts and push for Mueller's removal, according to one of the people familiar with the matter. McGahn put off making the call because he disagreed with the strategy, the person said. When Trump persisted in pressing the issue, McGahn told other senior White House officials he would resign if Trump didn't back off. Trump let the matter drop, the person said. Trump cannot directly fire Mueller. Any dismissal, for cause, would have to be carried out by Rosenstein, who appointed the counsel and has continued to express support. Trump has fumed to confidants that the Mueller probe is 'going to choke the life out of' his presidency if allowed to continue indefinitely, according to an outside adviser who spoke on condition of anonymity to discuss private conversations with the president. Likely contributing to Trump's sense of frustration, The New York Times reported last week that Mueller had subpoenaed the Trump Organization for Russia-related documents. Trump had said Mueller would cross a red line with such a step. 'Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans?' he tweeted Sunday. Some of Mueller's investigators indeed have contributed to Democratic political candidates including Hillary Clinton, but Justice Department policy and federal service law bar discrimination in the hiring of career positions on the basis of political affiliation. Mueller is a Republican. ___ Associated Press writers Lisa Mascaro, Darlene Superville and Eric Tucker in Washington contributed to this report.