Mr Bush had earlier accused the Democrats of denying him the flexibility he needs to protect the country and the American people.
The President is blaming the Democratic-led Senate of holding up his plans to create a new Homeland Security Department.
Their verbal clash occurred at an event to mark the 75th anniversary of Mount Rushmore - the huge memorial to four of America's greatest leaders carved into a mountainside in South Dakota.
Under the granite stare of his predecessors, President Bush said he needed flexibility.
"I don't want to have my hands tied so we cannot do the number one job you expect, which is to protect the homeland," he said.
New vigour
The Democrats have sparred with Mr Bush over the proposed 170,000-strong department - particularly the administration's authority to hire and fire employees.
But responding after the speech, Tom Daschle - who is a Senator for South Dakota - said he did not want to give "this president or any president dictatorial powers that compromise the checks and balances that our founding fathers recognised".
He said the president should not have a right to "fire an employee on the spot" or to move resources without congressional approval.
The BBC's Justin Webb in Washington says that although the argument is over a relatively mundane subject, Mr Daschle's choice of words suggests that the Democrats are abandoning their defensive political posture.
They are ready now to take on the President with a vigour not seen since 11 September, our correspondent adds.