Sen. Lamar Alexander, R-Tenn., wants a key Senate committee to put together a narrow bipartisan stabilization package for Obamacare by the end of next week.

Alexander is chairman of the Senate Health, Education, Labor, and Pensions Committee, which will be crafting the package. The panel is holding the first in a series of hearings on how to stabilize the individual market, which includes Obamacare's exchanges and is used by people that don't have insurance through a job or the government.

"Timing is a challenge," Alexander said in a copy of his opening remarks for the first hearing on Wednesday. "So I propose that we come to a consensus by the end of next week when our hearings are complete so that Congress can act by the end of September."

Alexander called for giving states more flexibility from Obamacare's requirements, including essential health benefits that Obamacare plans have to cover. However, he stressed the states can't "reduce the patient protections most of us support, including protections for those with pre-existing conditions."

He also called for funding for one-year cost-sharing reduction payments to insurers to reimburse them for lowering out-of-pocket costs for low-income Obamacare customers.

Alexander said Senate HELP doesn't have a lot of time since insurers have to submit final rates by Sept. 20. Independent estimates say premiums could rise by nearly 20 percent without the insurer subsidies.

It remains unclear if the committee can get a deal within about a week and a half.

Ranking Member Sen. Patty Murray, D-Wash., wants to add funding for reinsurance, which props up Obamacare insurers with the sickest claims.

"I think we're all aware threading this needle won't be easy," Murray said in her prepared opening statement. "But I do believe an agreement that protects patients and families from higher costs and uncertainty, and maintains the guardrails in our current healthcare system, is possible."