After a week abroad, President Obama rejoins the health care debate this week with speeches in Michigan and New York, as he tries to keep the pressure on Congress to get a major overhaul moving this month.

Though critics say Obama needs to become more involved in day-to-day negotiations, the administration is leery of micromanaging the legislative process.

“Our team is working with members of Congress every day on this issue, and it is my highest legislative priority over the next month,” the president said when asked about health care during a news conference on July 10 in L’Aquila, Italy. “We are having a whole series of constant negotiations. ... This is different committees that have different priorities. My job is to make sure that I’ve set some clear parameters in terms of what I want to achieve.”

In the Senate, the Health, Education, Labor and Pensions Committee is likely to finish work this week on an overhaul bill that would require most Americans to obtain health insurance, either through their employers or from a menu of choices that would be available in each state, including a government-run plan.

Employers with more than 25 workers would have to offer subsidized health insurance or pay a per-worker penalty. Most individuals without job-based insurance would have to get their own policies or pay a fine.

The HELP Committee bill has unified Democratic backing but no Republican support. GOP senators are focusing their efforts on a competing bill under negotiation in the Senate Finance Committee.

In the House, Democratic leaders hope to move their draft legislation through three separate committees this week. But they are facing intense uneasiness among their more conservative members over the roughly $1 trillion price tag of the package and proposals to help pay for it by a surtax on families making $350,000 or more per year.