A key House committee chairman Wednesday sharply criticized a wide-ranging immigration bill just passed by a Senate committee, underscoring the difficulties ahead as the politically volatile measure moves forward in a divided Congress.

Separately, a bipartisan House group that has been working behind the scenes to craft its own immigration measure encountered fresh difficulties.

House Judiciary Committee Chairman Bob Goodlatte, R-Va., argued that the bill passed by the Senate Judiciary Committee on a bipartisan vote Tuesday “falls far short” of what is needed to end the problem of illegal immigration, and is unlikely to secure the border.

“While I commend the Senate for their continuing efforts to tackle the extremely difficult task of reforming our broken system, I must observe that S. 744 repeats many of the mistakes of the past,” Goodlatte said at a hearing of his committee on the legislation. “We have serious concerns.”

Goodlatte’s critique was echoed by other Republicans on his panel. “I cannot find any deadline by which the border needs to be secure” under the legislation, complained Rep. Lamar Smith, R-Texas.

Their comments came the day after the Senate Judiciary Committee voted 13 to 5 to advance the measure to the full Senate, with three Republicans joining the Democratic majority. The bill would aim to enact new border controls and enforcement mechanisms in the workplace, allow tens of thousands of workers into the country legally for high- and low-skilled jobs, and create a 13-year path to citizenship for the 11 million people already here illegally.

Senate Majority Leader Harry Reid, D-Nev., pledged Wednesday to bring the measure to the Senate floor in June after Congress returns from its Memorial Day recess. Minority Leader Mitch McConnell, R-Ky., said he would support a vote to begin debate on the measure, although he said he remained undecided about supporting it.

“I’m undecided about the bill, but I’m not undecided about the problem,” McConnell said on Fox News Channel. “The border is unsecure and we need to fix it. So I’ve not decided yet whether this is the bill to do that, but we’ve got a serious problem along the border.”

Meanwhile there were new setbacks for a bipartisan House group that has been working to finalize its own measure along the lines of the Senate bill.

The group of eight lawmakers, four Democrats and four Republicans, has been promising for months to release the legislation but has encountered numerous difficulties as it tries to get a deal that could get through the Republican-controlled House while also satisfying Democratic concerns. Late last week, after reports that talks had stalled, lawmakers insisted they had an “agreement in principle.” But on Wednesday lawmakers and aides said the group had new problems arising from a dispute over how to handle health care for immigrants here illegally.

Republicans in the group are trying to establish a system to ensure that no taxpayer money goes to pay for health care for people here illegally. Democrats in the group thought they had come up with a mechanism that could satisfy that concern at least well enough to act as a placeholder so the group could release the legislation, two House aides said, speaking on condition of anonymity to discuss the private deliberations.

But, according to the aides, House Democratic Leader Nancy Pelosi, D-Calif., and other Democratic leaders objected over concerns that the legislation moved too far to the right and into areas outside of the purview of the immigration group.