Billionaire-turned-politician Trump (35 per cent) has a 17-point lead over his closest rival Cruz (18 per cent), ahead of Saturday's primary.
Ohio Governor John Kasich (11 per cent) and Florida Senator Marco Rubio (12 per cent) are in a virtual tie for the third spot, CBS News said in its poll.
However, in a Fox News poll - also released this morning - Trump's lead over Cruz is reduced to 13 percentage points, still considered to be very high.
As per the average of all major polls compiled by RealClearPolitics.Com, Trump (34.1 per cent) has an advantage of nearly 16 per cent against Cruz (17.6 per cent).
Meanwhile, for the first time, Trump has fallen behind Cruz in a national survey, according to the Wall Street Journal-NBC News poll.
Even though it falls within the margin of error, the poll released yesterday showed Republican Cruz (28 per cent) now leads nationally ahead of Trump's 26 per cent.
During a CNN-organised town hall, Cruz, a top attorney, said he would himself argue the case in court against Trump.
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