Senate Majority Leader Mitch McConnell is tempering expectations for passing an Obamacare replacement bill in the Senate any time soon.

“This is a really tough issue,” McConnell told Bloomberg News. “You all covered extensively the difficulty of getting a bill out of the House. It won’t be any easier getting it out of the Senate.”

McConnell acknowledged concerns that many senators have with the bill that the House passed earlier this month. The House bill’s approach to Medicaid and to protections for people with pre-existing conditions are flashpoints for many senators.

The House bill would not only roll back the Affordable Care Act’s Medicaid expansion, it would cut more than $800 billion over 10 years from Medicaid and cap its federal funding for the first time. Many senators have problems too with a provision added to the House-passed American Health Care Act that would allow insurers to charge more to people with preexisting conditions if their states opted out of provisions in the ACA barring such decisions. In the House plan, the states that opted out would have to set up “high-risk pools” to absorb some of the costs of caring for people with pre-existing conditions.

Sens. Susan Collins (R-ME) and Lisa Murkowski (R-AL) have also been on record opposing the provision in the House bill that would cut off federal funding for Planned Parenthood.

McConnell and other Senate leaders have suggested that the bill the Senate takes up may look very different from the House bill. Senate Finance Committee Chairman Orrin Hatch (R-UT) said this week that there have been discussions of keeping the Affordable Care Act’s individual mandate, which requires all Americans to have health insurance, until 2020. Keeping portions of the ACA in place temporarily would also likely mean keeping the law’s taxes in place, lawmakers have said.