A majority of Canadians don't support corporate tax cuts and are opposed to buying the F-35 fighter jets, two major pieces of the Conservative government's plan for the country, a new poll suggests.

In a new poll conducted for CBC News following the May 2 federal election, 53 per cent of people surveyed said they were opposed to dropping the corporate tax rate from 16.5 per cent to 15 per cent. About two-fifths — 39 per cent — agreed with the cut and eight per cent weren't sure.

Just more than half — 52 per cent — said Canada should not go ahead with the purchase of 65 F-35 fighter jets, while 37 per cent polled said the government should buy the planes. Twelve per cent said they didn't know.

Environics polled 2,000 people by phone from May 12 to 22, with a margin of error of plus or minus 2.2 percentage points.

Solid support for Senate reform

When it comes to other issues the Conservatives campaigned on, reforming the Senate had the most solid support: 65 per cent of those polled agreed with putting an eight-year limit on Senate appointments, with only 24 per cent disagreeing.

People were more evenly split on ending the long gun registry, however, with 46 per cent of those surveyed saying the government should not eliminate it. Only slightly less — 43 per cent — said Canada should get rid of the registry, and 11 per cent said they didn't know.

Keith Neuman, group vice-president of public affairs at Environics, says a lot of these issues were contentious before the election. They're fairly specific policies, rather than big picture initiatives, possibly explaining the split in opinion.

"With the exception of Senate reform, these were not big vote getters. These were not broadly popular themes. They did not capture the aspirations or values of a huge segment of Canadians," he said.

"These are issues for which there was not a lot of public groundswell of support to begin with, and the Conservatives and [Prime Minister] Stephen Harper probably understood that, but they knew it would play to their constituents and that worked to get them where they need to go."

Ending the per-vote subsidy for political parties, something Harper tried to do in 2008 before facing such a backlash from opposition parties that he almost lost power, also drew a split result in the poll.

Two-fifths of Canadians polled, or 40 per cent, said the government should leave the $2 per vote subsidy in place. Slightly more — 42 per cent — said Harper should continue with his plan to eliminate it, while 18 per cent said they didn't know.

The Conservatives have promised to kill the subsidy now that they have a majority government.

Opposition to changing health care

Despite the even split on a number of issues, the poll showed opposition to more private payment for health-care services is strong.

More than two-thirds of Canadians surveyed said they want the government to continue covering the majority of health-care costs, with 69 per cent saying Canada should not move toward more costs being paid for by individuals and private insurers.

A quarter said they wanted individuals to start paying more.

Among those who reported voting Conservative, 65 per cent want to see the government continue to cover most of the costs. The vast majority of opposition party supporters agreed, with 82 per cent of Liberal voters and 76 per cent of both NDP and Bloc Québécois voters saying no to increasing private payment.

"Canadians continue to believe in the system they have. They recognize there are problems. They are concerned about the broad picture... but by and large they still believe and largely have confidence in the system. It is still a source of identity and pride," Neuman said.

No support for left-wing merger

The poll also found little support for a merger between the NDP and Liberal Party, an idea that re-surfaced after the Liberals lost official opposition status in the House of Commons.

Three-quarters of NDP polled and 72 per cent of Liberals said they oppose a merger between the two parties. The majority of Bloc voters — 64 per cent — and 82 per cent of Conservative voters agree the two should remain separate. The Conservatives are thought to benefit from vote-splitting between the two left-of-centre parties.