But he says that as a senator, he has "grave concerns" about letting a president weaken Congress' power of the purse.
If Senate Democrats are united, they will need only four Republican defections to pass the a rejection of his Trump's emergency declaration and send it to his desk. "We have too many smart people that want border security, so I can't imagine that it could survive a veto", Trump told reporters in the Oval Office last Friday.
If passed by the House, the resolution will hit the Senate floor to be voted on within 18 days.
"Under no plausible assessment of the evidence is there a national emergency today that entitles the president to tap into funds appropriated for other purposes to build a wall at the southern border", the group said in the letter, which will be entreated into the Congressional record Monday.
Even so, the votes are posing tricky decisions for GOP lawmakers from swing states, where Republican voters are divided between Trump loyalists and those with more moderate views.
Tillis says he will vote for the resolution if it comes before the Senate, emphasizing, "As a conservative, I can not endorse a precedent that I know future left-wing presidents will exploit to advance radical policies that will erode economic and individual freedoms".
Pakistan says Indian aircraft 'released a payload' after crossing frontier, no casualties
The Indian rupee weakened offshore, with one-month non-deliverable forward trading at 71.32 a dollar before local markets open.
House Minority Leader Kevin McCarthy, R-Calif., said enough Republicans would support Trump's emergency that the House won't be able to muster the two-thirds majority required to override a veto.
A group of 23 former Republican members of Congress have written a letter urging a termination of the emergency declaration.
The US Congress braced for an unprecedented effort to overturn a presidential emergency declaration, as Republicans worked to limit defections on the eve of a critical House vote while Democrats framed the issue as a constitutional showdown.
Conservatives rightfully cried foul when President Barack Obama used executive action to completely bypass Congress and unilaterally provide deferred action to undocumented adults who had knowingly violated the nation's immigration laws.
Sen. John Cornyn, R-Texas, a close adviser of McConnell, said in a brief interview that the Senate would vote on the emergency declaration sometime in the next three weeks.