AFTER SPENDING THE WINTER managing state budget shortfalls and snow emergencies, Gov. Charlie Baker weathered his first 100 days in office remarkably well, according to a new poll that shows the governor riding sky-high approval ratings that make him the most popular politician in the state.

Voters also narrowly oppose the concept of Boston hosting the 2024 summer Olympics, with 43 percent of those surveyed statewide supporting the bid and 46 percent against. That result was within the poll’s margin of error.

Baker’s favorability rating of 74 percent put him ahead of both Boston Mayor Marty Walsh (59 percent) and US Sen. Elizabeth Warren (54 percent), and 70 percent of voters polled by Suffolk University’s Political Research Center approved of his job performance compared to just 6 percent who disapproved.

Only 8 percent of voters polled said they had an unfavorable opinion of Baker, which could bode well for the governor as presses his case on the Democrat-controlled Legislature for his budget priorities and a bill he will file Wednesday overhauling the management structure of the MBTA.

Baker’s predecessor, Gov. Deval Patrick, had a favorability rating of 53 percent at this point in his first term in 2007 after a series of early stumbles. Over 42 percent said Baker is a better governor than Patrick, while 30 percent were undecided. Forty-nine percent rated Baker’s performance thus far as average, and 39 percent said he has performed above average.

Given a list of 21 issues, voters identified the state budget as the issue of most importance to them at 22 percent followed by 16 percent who said jobs and the economy, 11 percent who said fixing the MBTA, and 7 percent who said taxes.

“Charlie Baker has had a near-perfect 100-day start with very few early mistakes,” Suffolk pollster David Paleologos said in a statement. “During that time record-breaking snowfall has been converted to record-breaking poll numbers as Baker’s leadership during the crisis has voters of all parties giving him high marks. Unless he keeps up this amazing pace, probability says that from this point on his numbers can only go in one direction and will settle down at some point.”

The Suffolk poll surveyed 500 voters between April 16 and April 21 and had a margin of error of 4.4 percent.

Predictably, confidence in the MBTA after a winter of service failures suffered with 73 percent of voters rating the agency as fair or poor and only 12 percent rating the transit agency excellent or good.

On the Olympics, 78 percent of those surveyed favor a ballot question to gauge support for hosting the games. The organizers of the Olympic bid – Boston 2024 – have committed to following through with its international bid only if voters register support through a ballot process.

Asked about support for the games if there were a requirement that no public funding be involved, 56 percent of voters said they would support hosting the games. Organizers, who are still developing critical details of their bid, have said the public money required to host the games would be limited to federal support for security and state spending on infrastructure projects that are already in the state’s long-term plan for public transit and transportation.

Fifty-three percent said hosting the Olympics would help the state economically, while 35 percent said it would hurt.

The penalty phase in the trial of DzhokharTsarnaev, convicted on 30 counts related to the 2013 bombing of the Boston Marathon, started on Tuesday, with the 21-year-old facing either the death penalty or life in prison without parole.

Of those surveyed, 58 percent said Tsarnaev should receive life in prison, while 33 percent favored the death penalty. Though Massachusetts does not have a law authorizing the death penalty and public support for that punishment has waned, 47 percent said they would be willing to impose the death penalty in this case, while 45 percent said they could not.

Nearly 57 percent of those polled said Massachusetts was moving in the right direction, with a plurality of 47 percent identifying Baker as the most powerful politician on Beacon Hill followed by House Speaker Robert DeLeo at 13 percent. Less than 2 percent said they thought new Senate President Stanley Rosenberg wielded the most clout under the golden dome.

Baker’s standing on women’s issues polled well also, with 62 percent saying they trust Baker to stand up for women’s rights and issues of importance to women compared to just 15 percent who said they do not trust Baker on those issues.