Story highlights GOP lawmakers are feeling the heat to show how they would replace Obamacare

Former President Barack Obama's signature health care law covers some 20 million people

(CNN) Two Republican senators introduced legislation Monday to replace Obamacare amid mounting pressure on the GOP to craft an alternative to the massive healthcare law.

Sens. Bill Cassidy of Louisiana and Susan Collins of Maine unveiled a bill that they are describing as an "Obamacare replacement plan." The duo is promising that the proposal would give more power to the states on health care policy, increase access to affordable insurance and help cover millions of Americans who are currently uninsured.

At the core of their proposal: Any state that likes Obamacare can keep it.

"Republicans think that if you like your insurance, you should keep it. And we mean it," Cassidy said. "They could opt to stay in Obamacare or they could opt for no federal help. So, California and New York, you love Obamcare? You can keep it."

It is not clear whether the legislation, which is based on a measure Collins and Cassidy introduced in 2015 and has a companion bill in the House from Rep. Pete Sessions, would garner backing from party leadership.

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