Trump is also dividing Americans across party lines more than any recent president, as nearly all Republicans support him and nearly all Democrats oppose him.
On the other hand, the Rasmussen poll showed that only 45 percent of Americans disapproved of the president and 36 percent felt strongly about their disapproval.
After Senate Majority Leader Mitch McConnell invoked a rarely used rule, the Republican-majority in the Senate voted that Warren was to be barred from further debate related to the nomination of Jeff Sessions as attorney general.
Voters also say Obama's legacy is likely to improve, with 47 percent saying they think he will go down as an outstanding or above average president.
The poll, conducted February 9-10 with 1,791 registered voters, has a margin of error of plus or minus 2 percentage points.
The intensity of the public's early views of Trump is striking: Fully 75% either approve or disapprove of Trump strongly, compared with just 17% who feel less strongly.
Only 71 percent of respondents who voted for Trump in 2016 supported Trump in the poll, and he lost ground with 10 percent of Independent voters, as well.
Results of the poll - conducted on February 9 and 10 - came just days after Republican senators issued a gag order on Warren, banning her from participating in a debate regarding then-Sen. The only occasion when strong disapproval of George W. Bush was higher than for Trump now was in December 2008, near the end of his presidency.
Sixty-one percent said the president should avoid criticizing companies, while 27 percent found that to be acceptable behavior. "The slate of bad news for the administration is catching up to him, although it's important to note that his approval rating remains sky-high among people who voted for him in November".
21 percent have a favorable view of Trump's top adviser Steve Bannon, while 33 percent have an unfavorable opinion of him.
While the numbers have Trump beating Warren, it shows he would lose to a generic Democratic candidate.
But a conflicting poll from Pew Research shows the president's approval rating has fallen to just 39%, 16 points below Rasmussen's survey, which questions 500 people per night on a three-night rolling basis.