However, the steady stream of news about investigations into those contacts doesn't appear to have affected President Donald Trump's approval rating, which ticked up only one percentage point -- 44% to 45% -- from January.
Concerns about the reported contacts are closely tied to partisanship, with 71% of Democrats saying they are "very concerned" about it while 54% of Republicans say they have no concerns "at all" about the reports.
Among Republicans, a majority feel Congress can handle the investigation, but a sizable 43% support the call for a special prosecutor, as do majorities of Democrats (82%) and independents (67%). Overall, the poll finds that 65% would rather see a special prosecutor handle the investigation, while 32% think Congress is capable of handling it.
Views of whether Russia attempted to influence the US election at all are becoming increasingly polarized when compared with a January CNN/ORC poll. In the new survey, more Democrats say it's extremely likely that the intelligence community's assessment that Russia did attempt to influence the US election is correct than said so before the inauguration (47% in January, 52% now) while more Republicans now say that it's not at all likely to be correct (from 12% in January to 27% now).
And more now see Russia as a threat to the United States than said so last spring, before any news about Russia's attempted interference in the election emerged.
In the new survey, 34% call Russia a "very serious" threat, up from 21% in May 2016. Last spring, Republicans were about twice as likely as Democrats to consider Russia a deep threat (30% among Republicans, 15% among Democrats). Now, that's reversed, with Democrats about twice as likely to consider Russia a very serious threat (51% among Democrats, 24% among Republicans).
Approval ratings remain steady
None of this, however, appears to have taken a toll on Trump's approval ratings. Both the president's approval rating and favorability rating have held steady through the early days of his presidency.
According to the poll, 45% approve of Trump's handling of the job, about the same as the 44% who said so in early February, and 45% say they have a favorable view of the President, just about the same as the 44% who said so in January.
Speech didn't change things
At the same time, the steady numbers suggest Trump's well-received address to Congress last week hasn't provided a boost to the president's numbers.
The poll, conducted entirely after Trump spoke to Congress last Tuesday, finds the share who say his proposed policies will move the country in the right direction in about the same spot as January, 49% now vs. 48% then. And 53% say Trump's policy priorities do not reflect their own, while 46% feel he is emphasizing policies that reflect their own priorities.
Economy the only strong issue for Trump
At the same time, Trump's approval rating for handling the economy has increased to 55%, up from 49% a few weeks into his tenure.
The economy, which 26% of Americans call the most important issue facing the country, remains his strongest issue, as it was throughout the 2016 campaign. It is the only issue tested where Trump earns clearly positive reviews.
Trump's ratings shift negative on several issues on which he's made efforts to reverse the course of Obama-era policies at the start of his presidency: Health care (53% disapprove, 43% approve), immigration (55% disapprove, 44% approve), environmental policy (52% disapprove, 42% approve) and foreign affairs (54% disapprove, 41% approve) among them.
Ratings of Trump's handling of military issues are mixed, with a near even split on national security (50% approve, 49% disapprove) and a slight negative tilt on handling the role of commander in chief (51% disapprove, 47% approve).
As Trump's budget plan begins to roll out, almost 1 in 10 remain unsure of his handling of the budget and taxes, higher than on other issues. Those who do express an opinion split on his handling of the budget (47% approve, 46% disapprove) and tilt negative on taxes (48% disapprove, 43% approve) and helping the middle class (50% disapprove while 45% approve).
Pence, Congress improve
Vice President Mike Pence's favorability rating has ticked upward since the inauguration; 47% have a favorable view and 37% unfavorable, compared with a 40% favorable to 37% unfavorable split in January.
And approval toward Congress has also climbed, up to 28% from 20% in January, reaching its highest level since 2009.
The CNN/ORC Poll was conducted March 1 through 4 among a random national sample of 1,025 adults. Results for the full sample have a margin of sampling error of plus or minus 3 percentage points. Error margins are larger for subgroups.