COLORADO SPRINGS, Colo. (Reuters) - Officials with the conservative U.S. political network overseen by the Koch brothers say they are unhappy with the healthcare bill that may be voted on by the Senate this week and will lobby for changes to it.

FILE PHOTO: An Americans for Prosperity banner is seen during an event in Manchester, New Hampshire, July 22, 2015. REUTERS/Dominick Reuter

At a weekend event with conservative donors, top aides to Charles Koch, the billionaire energy magnate, said the Senate bill does not go far enough to dismantle former President Barack Obama’s signature healthcare law, also known as Obamacare.

“We have been disappointed that movement has not been more dramatic toward a full repeal,” said Tim Phillips, president of Americans for Prosperity, a grassroots advocacy group backed by Charles Koch and his brother, David.

The Senate’s 142-page proposal, worked out in secret by a group led by Senate Majority Leader McConnell, aims to deliver on a central campaign promise of President Donald Trump to repeal Obamacare, which has provided coverage to 20 million Americans since its passage in 2010.

Republicans view the law, formally called the Affordable Care Act, as a costly government intrusion and say individual insurance markets created by it are collapsing.

Phillips and other aides to the Koch network told Reuters they want to see the Senate bill do more to roll back Obamacare’s expansion of the Medicaid program for poor and disabled Americans. They also contend the bill does not do enough to reform the U.S. healthcare system and cut costs.

The aides said lobbying efforts to reshape the bill are continuing ahead of a planned vote.

Similar concerns helped steer the House’s version of the bill in a more conservative direction. A primary mover of that effort, Mark Meadows, a Republican congressman from North Carolina, attended the Koch donor event.

Meadows, chairman of the conservative Freedom Caucus in the House, said he is prepared to support the Senate bill if it clears that chamber, a sign that quick action to land the legislation on Trump’s desk is possible.

However, Meadows said the Senate version of the bill would need to be amended to allow insurers who sell plans on Obamacare’s insurance exchanges to offer less-expensive plans that do not comply with that law’s coverage requirements.

Republican Senator Ted Cruz of Texas, who currently opposes the Senate bill, has offered an amendment along those lines. Cruz attended the Koch event here, as did Senators Jeff Flake of Arizona and Ben Sasse of Nebraska, who remain undecided.

Meadows also seeks an amendment that would allow some consumers who have private health savings accounts to deduct the cost of insurance premiums from their taxes.

Senate leaders have set a goal of passing the healthcare measure by the end of this week, ahead of the July 4 congressional recess, which would then send it back to the House.

If the Senate passes legislation this week that is palatable to the House, Meadows said it is conceivable the House could pass that version and choose to forgo a formal conference committee that would reconcile the Senate and House bills. That, he said, could result in sending the bill to Trump’s desk for his signature before the recess.

Getting a vote by the end of the week could be difficult.

Five Senate Republicans, including Cruz, have publicly voiced their opposition to the current Senate draft. No Senate Democrats are expected to back it, which means McConnell cannot afford to lose more than two Senate Republicans.

As a sign of the Koch network’s influence, Phillips said his organization is prepared to spend as much as $400 million before next year’s congressional elections to advocate for the network’s conservative causes.