The Official Opposition has been pushing the prime minister to enter into consultations with the provinces for the abolition of the Upper House. However, there would be more required than just a push to convince the provinces. Normally, the Senate only has a 180-day suspensive veto when it comes to constitutional amendments. After those 180 days have passed, the House of Commons can re-adopt a proposal and send it directly to the viceroy, without the consent of the Senate.
It is believed that, in the reference question referred to it by the Government, the Supreme Court of Canada will rule that the abolition of the Senate would require the consent of all ten legislatures of the provinces, and that the 180-day suspensive veto of the Senate would not apply (i.e., that the Senate would have an absolute veto over a proposal on whether it should be abolished).
The comprehensiveness of the Senate's integration into the Canadian constitutional framework would also pose a significant challenge to constitutional change. Even the distribution of seats in the House of Commons depends on the structure of the Senate for its seat guarantees in smaller provinces. Such a change would also affect the powers of Her Majesty the Queen of Canada to expand the Senate upon viceregal recommendation, and the Governor General to appoint senators.
Value of Bicameralism
The particular politics of the Senate notwithstanding, the values of bicameralism are clear. The rushed and hyper-political work of the House of Commons must be reviewed with a critical lens, technically corrected and, at times, fully revised or rejected upon closer scrutiny. The majority is not always correct, even when electorally-backed, and so this mechanism to slow things down and take a more critical look at fast-moving proposals is essential to healthy and responsible decision-making.
Possible Changes to Practice
One of the possible changes to the way that the Senate works that constitutional experts have agreed is entirely within the authority of the Government to make without a bona fide constitutional amendment would be the establishment of an "independent appointments commission" to provide non-binding advice to the prime minister on who ought to be nominated to a place on the Senate.